# Tagged Questions

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 ...
140 views

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 ...
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 ...
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? $$4x^2+4y^2+24x-16y+41=0$$
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 $$x^2 + y^2-4x+10y+26=0$$
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 ...
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 ...
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 ...
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: ...
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?
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 ...
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 ...
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: $(x-a)^2 + (y-b)^2 = r^2$
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 $a_i$, $b_i$ ...
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 ...
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 ...
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 ...
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. ...
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. ...
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 ...
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 ...
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?
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 $x^2 + y^2 -6x + 10y + 9 = 0$
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 ...
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. $\sqrt{(n_1-x)^2+(n_2-y)^2}=n_3$ ...
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? ...
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 ...