Q:

Derive the equation of the parabola with a focus at (4, −7) and a directrix of y = −15. Put the equation in standard form. (2 points) Question 5 options: 1) f(x) = one sixteenth x2 − 8x + 11 2) f(x) = one sixteenth x2 − 8x − 10 3) f(x) = one sixteenth x2 − x + 11 4) f(x) = one sixteenth x2 − x − 10

Accepted Solution

A:
Answer:[tex]\frac{1}{16} x^2-\frac{1}{2} x-10[/tex]Step-by-step explanation:When (x,y) is a point on the parabola, the distance from the focus is equal to its distance from the directrix.Given point as (4,-7) and  directrix as y=-15 then;distance to focus=distance to directrixApply formula for distance[tex]\sqrt{(x-4)^2+(y+7)^2} =(y+15)[/tex]square both sides[tex](x-4)^2+(y+7)^2=(y+15)^2\\\\\\x^2-8x+16+y^2+14y+49=y^2+30y+225\\\\\\\\x^2-8x+y^2-y^2+14y-30y+16+49-225=0\\\\\\16y=x^2-8x-160\\\\y=\frac{1}{16} x^2-\frac{1}{2} x-10[/tex]