Find the standard formof the equation of the parabola satisf

Find the standard formof the equation of the parabola satisfying thegiven equations.

Vertex: (5,-1); Focus: (5,-2)

The standard form of the equation is?

Solution

Vertex: (5,-1) and focus :(5,-2)

The vertex form of parabola is

y=(1/4p)(x-h)²+k

Where Vertex is (h,k) and focus is (h,k+p)

On comparing the given values of vertex and focus we get

h=5 , k=-1,k+p=-2

From k=-1 and k+p=-2 we get p= -1

Therefore the equation of parabola is

y=(1/-4)(x-5)²-1

-4(y+1)=x²+25-10x

-4y-4=x²+25-10x

y=(x²+25-10x)/(-4)

y=-x²/4 -25/4   + 5x/2