Tagged Questions

3
votes
2answers
35 views

What is the rationale for the factor of $4$ in the Conics parabola equation?

The Conics form of a parabola equation is $4p(y-k)=(x-h)^2$ where $(h,k)$ is the vertex of the parabola and $p$ is the distance from the vertex to the focus. (Which is also the same distance from the ...
1
vote
1answer
44 views

Turning an ellipse into a parabola

Today I was discussing circles, ellipses, hyperbolas, and parabolas in my precalculus class. We did the usual: completing the square, finding the center and radius (radii), etc. etc. But I like to ...
0
votes
2answers
38 views

Write the equation of an ellipse

The information given is the focus at (-2,3), directrix y=0 and eccentricity =1/2
2
votes
3answers
48 views

Find at least two ways to find $a, b$ and $c$ in the parabola equation

I've been fighting with this problem for some hours now, and i decided to ask the clever people on this website. The parabola with the equation $y=ax^2+bx+c$ goes through the points $P, Q$ and $R$. ...
0
votes
0answers
40 views

Generating parabola from points applet

Does anyone know of an applet or something that generates a parabola (graph and/or equation) given three (unique, non-colinear) points? I'm going to be mentioning this fact to my students as an aside ...
0
votes
1answer
46 views

In an equation that looks like the standard form of an ellipse, what must the constant on the RHS equal for exactly one solution?

I am working on a homework question: What must be the value(s) of $c$ for the following equation to have exactly 1 solution? The equation is of the standard form of the equation for an ellipse, ...
0
votes
2answers
41 views

Finding An Equation For A Parabola

The information given in this particular problem: Axis is parallel to y-axis; graph passes through and $(4,11)$.$(3, 4)$ $(0,3)$ From this information, I know that it opens either upwards or ...
1
vote
2answers
112 views

Derivation Of A General Equation Of An Ellipse

I am currently reading the topic alluded to in the title of this thread. In my textbook, after the equation has been derived, $\Large\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, it says by finding the ...
1
vote
1answer
88 views

An ellipse in the rhombus

Suppose that there is an ellipse that meets with the square, but exactly inside the rhombus. The rhombus's side would be some $x$ cm. (for e.g., we can take it as $2 \ cm$.) The ellipse would have a ...
2
votes
1answer
387 views

How to calculate minimum distance between two arbitrary ellipses in 2D?

Arbitrary ellipses means that they can be scaled, translated and rotated in any way in 2D. Do you know some high-school method (might be slightly more advanced than that) to find the minimum distance? ...
1
vote
1answer
109 views

How to find intersection of an ellipse and a line that passes through the foci

There are two lines, parallel to the $x$-axis, which pass through the foci and intersect the ellipse at four points. How can I find the points of intersection? vertex: $(0,0)$ foci: $(0,10)$ and ...
8
votes
3answers
434 views

If two parabolas don't intersect, is there a line that doesn't intersect either of them?

Two parabolas in a plane are given, such that they don't intersect. Is it true that there is a line in plane such that doesn't intersect any of them?
1
vote
2answers
115 views

Parabola Question: How to derive an appropriate equation based on specific criteria?

I've seen similar questions, but none worded quite like what I'm asking here. I'm not a math major, so I may have follow-up questions if answers befuddle me. Scenario: I'm trying to emulate a ...
2
votes
3answers
239 views

Parabola question

$$ \large{ \text{Here are some instructions from the original question: } \ \\ } $$ $$ \large{ k \in \mathbb{Z} \ \ \land \\ f(x)=x^{2}-3x+k \ \ \land \ \ g(x)=x-2 \ \\ \text{And, there is NO any ...
1
vote
1answer
120 views

Trajectory Problem with Parabola

The height of an object is given by $$ h(x) = -0.005x^2 + x. $$ When does the object hit the ground? When does it attain its maximum height? What is its maximum height? I divided -.005/-1 to get ...
1
vote
1answer
329 views

Find intersection(s) between parametrized parabola and a line

I'm trying to find the value(s) of the parameter $t$ at the intersection point(s) between a 2D general parabola (as a parametric function of $t$) and a line whose equations can be derived from two ...
1
vote
2answers
412 views

Finding & Plotting equation of hyperbola given foci, and difference in distances between them.

I have to plot the hyperbola (3 of them actually) in MATLAB, and so it'd be good if I could find some sort of general formula. The foci do not necessarily have to be on the axes (e.g. $(5,3)$ and ...
3
votes
2answers
2k views

How do I find the equation of a tangent line to a curve?

I'm given $x^2+2x-4$ at $x=2$ and I have to find the tangent line to this curve at that point...
2
votes
1answer
116 views

Need help with the proof of conic section

Prove that the intersection of a plane and a object consist of one cone and one upside-down cone where the tip of cone meet is either degenerate conic or conic Also, idenify in what situation, the ...
2
votes
2answers
293 views

A hyperbola as a constant difference of distances

I understand that a hyperbola can be defined as the locus of all points on a plane such that the absolute value of the difference between the distance to the foci is $2a$, the distance between the two ...
4
votes
2answers
579 views

Find equation for hyperbola

Just taking (failing) a simple algebra class, can't figure this one out and no one can explain it to me and the book just tells me to do it. Find an equation for the hyperbola described: foci ...
4
votes
5answers
475 views

Usefulness of Conic Sections

Conic sections are a frequent target for dropping when attempting to make room for other topics in advanced algebra and precalculus courses. A common argument in favor of dropping them is that ...
6
votes
11answers
5k views

Derivation of the formula for the vertex of a Parabola

I'm taking a course on Basic Conic Sections, and one of the ones we are discussing is of a parabola of the form $y = a x^2 + b x + c$ My teacher gave me the formula: $x = -\frac{b}{2a}$ as the $x$ ...