Question

Write an equation of a parabola with vertex at(-10,-7)and the focus at (-10,-111/16)

Answer 1

The vertex form of parabola equation is y = a(x – h)2 + k, where (h, k) = vertex .

 

Where, vertex (h, k) = (-10, -7) and the point (x, y) = (-10, -111/16).

 

Substitute (h, k) = (-10, -7) and (x, y) = (-10, -111/16) in vertex form :: y = a(x – h)2 + k

 

-111/16 = a(-10 + 7)^2 - 7

 

-111/16 + 7 = a(-3)^2

 

(-111 + 112)/16 = a(9)

 

1/16 = a(9)

 

a  =  1/(16X9)

 

a  =  1/144

 

Substitute a = 1/144  and (h, k) = (-10, -7) in vertex form.

 

y = (1/144)(x + 10)^2 - 7

 

 

The parabola equation is y = (1/144)(x + 10)^2 - 7