# Tagged Questions

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### What are the coordinates of the ends of the latus rectum of the parabola $x^2 - 2y + 2 = 0$? [duplicate]

I've already graphed the parabola . i just don't know how to locate it's focus and the ends of it's latus rectum. On my graph, the vertex is on (0,1). Please help me with this. ASAP.
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### Show that endpoint of a focal chord is $$\left(\frac{4p^2}{x_0}, \frac{p^2}{y_0}\right)$$

If $PQ$ is a focal chord of the parabola $x^2=4py$ and the coordinates of $P$ are $(x_{0}, y_{0})$ show that the coordinates of $Q$ are $$\left(\frac{4p^2}{x_0}, \frac{p^2}{y_0}\right)$$ I labeled ...
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### ratio of tangent to the ellipse

The tangent at point $P = ( a \cos \phi, b \sin \phi)$ on the ellipse $\frac{x^2} {a^2} + \frac{y^2}{b^2}=1$ meets the $x$ and $y$ axes at the points $X$ and $Y$, respectively. Find in terms of ...
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### Find the equation of an ellipse given its focus, directrix and eccentricity

Ellipse has a focus $(3;0)$, a directrix $x+y-1=0$ and an eccentricity of $1/2$. Find its equation. I should probably use the fact that $r/d = e$, where $r$ is the distance from the focus to any ...
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### Convert ellipse parameter from General parametric form to General polar form

I am facing problem to convert ellipse standard parameters. Everything I say here is refer to http://en.wikipedia.org/wiki/Ellipse I know what are the General parametric form parameter . Lets call ...
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### Calculate perimeter from parametric form with an ellipse?

Suppose I have a thing such as an ellipse: $$\left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}=1$$ now we can define it so that $\frac{x}{a}=cos(\theta)$ and $\frac{y}{b}=sin(\theta)$. I ...
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### How to find orignal equations of type $y=ax^2+bx+c$. given 3 coordinate points?

Ok, simple question, having trouble understanding this in school. So given a set of 3 points (xy-plane), such as (40,30) (60,28) (20,25) i have to find the equation of the parabola. I ...
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### Hyperbola property

I am posting the following question under homework category. I hope I will have very good answer from mathematicians about conic sections. I have seen closely the conic sections and their ...
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### How to find points of tangency on a hyperbola?

If tangent lines to the hyperbola $9x^2-y^2=36 \;$ intersect y-axis at point $(0,6)$, find the points of tangency.
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### Tangent of an ellipse to an outside point

Let $C$ be a curve that is given by the equation: $$2x^2 + y^2 = 1$$ and let P be a point $(1,1)$, which lies outside of the curve. We want to find all lines that are tangent to $C$ and intersect ...
If I am given $V(8, -1)$ and $y_{intercept} = -17$, how would I go about finding the equation for that? Thank you very much!