equation of the parabola w/ vertex & focus coincide w/ the upper vertex and focus of the hyperbola x2/4-y2/9=1

Answer 1

The hyperbola

x²/4 - y²/9 = 1

a² = 4
a = 2
b² = 9
c² = a² + b² = 4 + 9 = 13
c = √13

Center is (h,k) = (0,0)

Foci are (h-c,k) and (h+c,k) which are (-√13,0) and (√13,0)

Vertices are (h-a,k) and (h+a,k) which are (-2,0) and (2,0)
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The parabola has vertex (2,0) and focus (√13,0).
p = √13 - 2

The equation of the parabola has the form:

4p(x - h) = (y - k)²

Plugging in values we have:

4(√13 - 2)(x - 2) = (y - 0)²
4(√13 - 2)(x - 2) = y²