Question

What is the equation of the quadratic graph with a focus of (8, −8) and a directrix of y = −6?

Answer 1

Answer:

$y=-\frac{223}{28}(x-8)^2-7$

Step-by-step explanation:

we are given a quadratic equation

we know that quadratic equation is same as equation of parabola

so, we can use formula

$y=a(x-h)^2+k$

Focus is

$(h,k+\frac{1}{4a} )$

now, we can compare it with given focus

=(8,-8)

we get

$h=8$

$k+\frac{1}{4a}=-8$

Directrix is

$y=k-\frac{1}{4a}$

we are given directrix =-6

$k-\frac{1}{4a}=-6$

we got two equations as

$k+\frac{1}{4a}=-8$

$k-\frac{1}{4a}=-6$

now, we can add both equations

and we get

$k+\frac{1}{4a}+k-\frac{1}{4a}=-8-6$

$2k=-8-6$

$2k=-14$

$k=-7$

now, we can find 'a'

$k+\frac{1}{4\times -7}=-8$

$k=-\frac{223}{28}$

now, we can plug back all values

and we get

So, equation of parabola is

$y=-\frac{223}{28}(x-8)^2-7$