Find the equation of the parabola described below Find the t

Find the equation of the parabola described below. Find the two points that define c the latus rectum, and graph the equation. vertex at (5, -1), focus at (5, -3) Choose the correct answer below. (x - 5)^2 = -8(y + 1) (y - 5)^2 = 8(x + 1) (y -5)^2 = -8(x + 1) (x - 5)^2 = 8(y + 1) The two points that define the latus rectum are

Solution

Since the x-coordinates of the vertex and focus are the same, they are one of top of the other, so this is a regular vertical parabola, where the x part is squared. Since the vertex is below the focus, this is a right-side up parabola and p is positive. Since the vertex and focus are -3 – (-1) = -2 units apart, then p = -2.

And that\'s all I need for my equation, since they already gave me the vertex(h,k) =(5,-1).

here x =5 same

(x – h)² = 4p(y – k)
(x – 5)² = 4(-2)(y + 1)
(x – 5)²= -8(y + 1)

endpoints of latus rectum: (h+2p), k±p)

:(5+2(-2) , -1+(-2)

end points are (5-4 , -3) and (5-4,1)

(1,-3) and (1,1)