0
votes
3answers
58 views

Find how far runners travel on a circular track (trig)

-How far has each runner traveled after 8 seconds? Though I just had to convert the rad/sec to rev/sec to get yards then multiply that by 8 seconds, but that isnt correct. Find the angle θ, in ...
1
vote
3answers
140 views

Tangents of circles

I'm trying to solve the following problem: Find the tangent equations of $x^2 + y^2 = 1$ which pass though point $(1, 2)$. As a line which goes though the point $(1, 2)$ is in the form $y = m(x - 1) ...
1
vote
1answer
28 views

Find Coordinates on a track

Charlie and Alexandra are running around a circular track with radius 60 meters. Charlie started at the westernmost point of the track, and, at the same time, Alexandra started at the northernmost ...
0
votes
2answers
41 views

Finding coordinates on a circle

So this problem I am have difficulty with. I think where I am going wrong is how to calculate the initial theta. Do I just use pi/2 because in the pictures it show to angle theta off the 90 degree ...
0
votes
1answer
62 views

Find angle in radians on a Ferris Wheel

John has been hired to design an exciting carnival ride. Tiff, the carnival owner, has decided to create the world's greatest ferris wheel. Tiff isn't into math; she simply has a vision and has told ...
1
vote
2answers
50 views

Finding the area of the shaded region on a circle.

So I need help finding the area of the shaded A region. I was going to do pi*(r^2)*(45/360) - (the area of the smaller triangle). I just dont know how to get the angle or the lengths of it. Is there ...
0
votes
1answer
34 views

Finding equations when given new center of a circle

$y = −x + \sqrt{2}$, $y = −x − \sqrt{2}$, $y = x + \sqrt{2}$, and $y = x − \sqrt{2}$. These equations determine lines, which in turn bound a diamond shaped region in the plane. Construct a diamond ...
1
vote
1answer
174 views

Finding the radius, distance of the center of circle inscribed in the square

I am trying to solve this question but can't figure out the last part. I was able to get answers for part A and B but i don't know how to approach/solve part C. Any help will be appreciated. The ...
0
votes
2answers
48 views

Question on inscribed equilateral triangle

Question: $ABC$ and $ODE$ are equilateral triangle with $BC || DE$. If $O$ is the center of the circle, then find the ratio $AQ:QC$ So, my thought on this is that, since we are not given the ...
0
votes
1answer
75 views

Find the shaded area

Find the shaded area Here is the equation that i've made \begin{align*} S&=\pi R^2\\ S_1&=\pi {R_1}^2\left(\frac{24}{360}\right)\\ S_2&=\pi{R_2}^2\left(\frac{24}{360}\right) \end{align*} ...
0
votes
4answers
62 views

Trouble in this circle question

Referring to this diagram (self-made): Question says: In the given figure diameter of the circle is $3$ cm. AB & MN are two diameter such that MN is perpendicular to AB. In addition CG is ...
0
votes
1answer
44 views

Simple arc/saggita/chord relation rearrangement

I'm stuck with something that I feel should be trivial. Consider the diagram on this page: http://mathworld.wolfram.com/CircularSector.html There are some pretty simple relations between the ...
1
vote
3answers
89 views

General form of a circle

My math teacher taught me that the general form (equation) of a circle is: $$ ax^2+by^2+cx+dy+e=0 $$ He also asked us this: If the product of $c$ and $d$ is negative, then what 2 quadrants can the ...
0
votes
1answer
45 views

Condition for this set of points

This is for a calculator experimental prob. simulation. So, there is circle in a square and the circle is touching all 4 sides of the square. We need to first choose a coordinate system (two ...
1
vote
1answer
71 views

Derivation of the length of an arc formula

My textbook says that the radian measure of an angle is the ratio: $\theta = \frac{s}{r}$ Where s is a portion of the entire circumference, and r is the radius. So essentially the arc length is thus: ...
5
votes
1answer
202 views

How is the Radian measure of angles derived/defined? [duplicate]

I'm currently studying the foundation of trigonometry (angles and their measures) and I've just been told that $\pi$ is the ratio of a circle's circumference to its diameter, so: $\pi =\dfrac ...
0
votes
3answers
109 views

Prove that a circle has an infinite number of tangents

It seems obvious that a circle is comprised of the set of all points that are equidistant from one point, and that each point on the circumference of the circle represents a tangent. This seems to ...
1
vote
0answers
143 views

Problems with Circles and Lines on a Cartesian Plane

(a) Find the equations of the two circles each of which touches both coordinate axes and passes through the point $(9,2)$. (b) Find the coordinates of the second point of intersection of the two ...
-1
votes
4answers
119 views

How do I find the center and radius of this circle? [closed]

How do I find the center and radius of this circle? $$4x^2+4y^2+24x-16y+41=0$$
0
votes
1answer
586 views

How do I find the equation of the line that passes through this circle?

Find the equation of the line that has x-intercept and passes through the center of the circle that has equation $$x^2 + y^2-4x+10y+26=0$$
3
votes
1answer
93 views

Perimeter of a rectangle with four circles in each corner

my teacher asked a question in exercise for calculate the perimeter of following: I get result of $144\pi$ and some of my friends got $208.2$ as result (assuming $\pi\approx3.14$). Q: what's the ...
1
vote
0answers
123 views

family of circles in bipolar coordinate system

I don't get the idea how the equation for this family of curve is $\displaystyle y^2 + (x - a \coth v)^2 = \frac{a^2}{\sinh ^2v}$ from this article on Wikipedia. Suppose, the equation is ...
1
vote
1answer
96 views

$\pi$ is just a number, or also the circumference of a sub-unit circle?

A unit circle defined in the Cartesian plane has a radius of $1$ and a diameter of $2$. So making a full round is $2 \pi$. Now, $\pi$ is the ratio of the circumference over the diameter, so if I have ...
2
votes
4answers
4k views

Finding the equation of a circle and a tangent line to the circle given two end points

Given the endpoints $(11, 23)$ and $(6, 13)$ of a circle, find the equation of the circle and the equation of a line tangent to the circle. First, I found the center using the midpoint formula: ...
0
votes
3answers
74 views

Circle- basic question [closed]

I know this is a basic question, but if I have a circle with radius 2 and I look at the area on the circle between angles $-\pi$ and $\pi$, will that be the bottom half of the circle?
1
vote
1answer
218 views

Equation of a circle with specific conditions

I am trying to find the equation for a circle that has the center at (-1 , 4) and passed through the point (3, -2) This seems like a straightforward problem. $$(x+1)^2+(y-4)^2 = 16$$ The radius ...
2
votes
3answers
140 views

How do I rearrange this formula? Circles around a larger circle.

My A-Level algebra is failing me. Can someone please tell me how to rearrange this formula to give $n$ when you know $R$ and $r$. $R \sin(180^\circ/n)/(1 - \sin(180^\circ/n)) = r$ This formula is ...
0
votes
1answer
102 views

Put this equation of a circle in its standard form

$ x^2 + y^2 = 4x+4$ How to put it in the standard form: $(x-a)^2 + (y-b)^2 = r^2$
2
votes
1answer
155 views

How to constrain disks that intersection of them is inside unit circle

I have two disks $(x-a_1)^2+(y-b_1)^2\leq r_1^2$ and $(x-a_2)^2+(y-b_2)^2\leq r_2^2$, where $a_1$, $b_1$, $r_1$, $a_2$, $b_2$, $r_2$ are all known. What kind of constraint can I put on $a_i$, $b_i$ ...
1
vote
1answer
614 views

Find distance traveled by tips of hands of clocks?

The short and the long hands of a wall clock are $8$ cm and $12$ cm respectively. Find the sum of the distance traveled by their tips in $3$ days. Give your answer in terms of $\pi$. My ...
5
votes
2answers
822 views

A circle is tangent to the $y$-axis at $y=3$ and has one $x$-intercept at $x=1$. Find the other $x$-intercept

A circle is tangent to the $y$-axis at $y=3$ and has one $x$-intercept at $x=1$. Find the other $x$-intercept Like previously mentioned, I'm not all too familiar with circles. So, I plotted the ...
3
votes
4answers
1k views

Find center, radius and a tangent to $x^2+y^2+6x-4y+3=0$

For the circle $x^2+y^2+6x-4y+3=0$ find a) The center and radius b) The equation of the tangent line at the point $(-2,5)$ Now, I solved a) and got the equation $$(x+3)^2+(y-2)^2=10$$ with ...
0
votes
2answers
218 views

Solving a set of “circular” quadratic equations

$x_a'$ and $y_a'$ are unknown. What's the simplest way to solve it? Every time I tried, it grew into tremendous size or was unable to think out in reasonable amount of time due to it's complexity. ...
1
vote
3answers
1k views

Polar equation of a circle

A very long time ago in algebra/trig class we did polar equation of a circle where $r = 2a\cos\theta + 2b\sin\theta$ Now I forgot how to derive this. So I tried using the standard form of a circle. ...
0
votes
1answer
844 views

Making a circle with paper folding, scissors, pencil, and a straightedge

Can we make a circle using paper folding, scissors, straightedge, anda pencil, allowing an infinite number of operations? I think my chemistry teacher have show me once how to make it during the ...
2
votes
3answers
439 views

How to normalize this circle equation?

I am given a circle described by the equation below. Is there any way I can bring it to the form $(x-a)^2 + (y-b)^2 = c^2$ to have it be normal? My intent is to translate it to polar coordinates and I ...
0
votes
1answer
72 views

Unknowns in Circle Equation

The circle $x^2-y^2 + ax -2y -15 = 0$ contains the point $P(-6, 5)$. How would I find a?
2
votes
3answers
4k views

Finding the center and radius of a circle given a general degree 2 equation

I am trying to find the center and radius of the circle with equation $x^2 + y^2 -6x + 10y + 9 = 0$
1
vote
6answers
49k views

Finding an equation for a circle given two points

No idea how to do this, I used to have these conic shapes committed to memory but I forget them already. I am supposed to find an equation for the circle that has center $(-1, 4)$ and passes through ...
2
votes
1answer
147 views

Intersections of 2 circles

Let me ask a similar question to the one I did yesterday. I got answers which said that the following problem had no general solution for x and y. $\sqrt{(n_1-x)^2+(n_2-y)^2}=n_3$ ...
9
votes
7answers
7k views

a circle graph is not a function?

I'm a little confused by the rule: If you draw a vertical line that intersects the graph at more than 1 point then it is not a function. Because then a circle like $y^2 + x^2 = 1$ is not a function? ...
1
vote
1answer
813 views

Area of a square using circle

So I have this square and theres a circle inside of it. The circle of radius $r$ is inscribed in the square. So how do I find the area of the square in terms of $r$? I know that area of a circle is ...
5
votes
12answers
8k views

how to find center of an arc given start point, end point, radius, and arc direction?

Given an arbitrary arc, where you know the following values: start point (x0,y0), end point (x1,y1), radius (r) and arc direction (e.g. clockwise or counterclockwise from start to end), how can I ...