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Find the equation of the parabola with focus on the line $y=x$ at $(h, h)$ and directrix with equation $y=-x-2 h .$ (The axis of the parabola is the line $y=x .)$

$$x^{2}+y^{2}-2 x y-8 x h-8 y h=0$$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Missouri State University

Campbell University

Harvey Mudd College

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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Find the focus and directr…

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02:03

Find the vertex and focus …

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mm. So for this problem we want to find the equation of the problem with a focused um on the line, Y equals X at H. H. And direct tricks. Um With the equation Y equals X my negative x minus two H. So we see that the axis of the problem is the line Y equals X. That's an interesting way of looking at it. We'll end up getting his X squared plus y squared right next to x y -8 x speech, mhm minus eight. Yh there are. And what we end up seeing as a result of this is that if we complete the square we would end up getting it in a more familiar form. We can see that as this H value increases. We see that the parabola um is has its access along and the way it was excellent.

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