Find an equation of the parabola with vertex (-3,5) and focus (-3,7)

Question

Just trying to find an equation for a parabola. stuck on a HW problem. could really use some help

Answer 1

vertex (-3,5) focus (-3,7) means the parabola is open upwards.

8(y-5)=(x+3)^2

vertex is on the curve, so it satisfies the equation.

8=4 times the distance between the focus and the vertex.

 

the 2 points share the x-value, so the axis of symmetry is x=-3, which is vertical.

focus is inside the curve, and vertex is on the curve. since 7>5, you know the curve opens upward, and the distance between the 2 points is 7-5=2.