Find the equation of the parabola with vertex at (8, 3) and which passes through (7, 5) and (7, 1).
A) $\quad ( y - 3 ) ^ { 2 } = - 4 ( x + 8 )$
B) $( y - 3 ) ^ { 2 } = - 4 ( x - 8 )$
C) $( y - 1 ) ^ { 2 } = 2 ( x - 7 )$
D) $( y - 3 ) ^ { 2 } = - 8 ( x - 8 )$
E) $( y + 3 ) ^ { 2 } = 4 ( x + 8 )$

Question

Find the equation of the parabola with vertex at (8, 3) and which passes through (7, 5) and (7, 1). 
A) $\quad ( y - 3 ) ^ { 2 } = - 4 ( x + 8 )$
B) $( y - 3 ) ^ { 2 } = - 4 ( x - 8 )$
C) $( y - 1 ) ^ { 2 } = 2 ( x - 7 )$
D) $( y - 3 ) ^ { 2 } = - 8 ( x - 8 )$
E) $( y + 3 ) ^ { 2 } = 4 ( x + 8 )$

Quizplus · Accepted Answer

The equation of a parabola with vertex (h, k) is given by (y - k)^2 = 4p(x - h), where p is the distance from the vertex to the focus or directrix. In this case, the vertex is (8, 3), so h = 8 and k = 3. The point (7, 5) is on the parabola, so we can substitute these values into the equation to get (5 - 3)^2 = 4p(7 - 8). Simplifying, we get 4 = -4p, so p = -1. Therefore, the equation of the parabola is (y - 3)^2 = -4(x - 8).

Find the Equation of the Parabola with Vertex at (8 (y−3)2=−4(x+8)\quad ( y - 3 ) ^ { 2 } = - 4 ( x + 8 )(y−3)2=−4(x+8)

Find the Equation of the Parabola with Vertex at (8 $\quad ( y - 3 ) ^ { 2 } = - 4 ( x + 8 )$