Question

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What is the equation for a parabola with a focus of (4,3) and a vertex of (4,1)

Answer 1

The vertex and focus of parabola lie on its axis.

Points (4,−3) and (4,−1) lie on the line x=4

So, the axis of parabola is the line x=4

Focus of the parabola lies below the vertex. So, the parabola is downwards opening

So, the equation of parabola is (x−4)

2

=−4a(y+1)

Distance between focus and vertex =−1−(−3)=2

∴a=2

Vertex of parabola is (4,−1)

So, the equation of parabola is (x−4)

2

=−4(2)(y+1)

⟹x

2

−8x+16+8y+8=0

⟹x

2

−8x+8y+24=0

Step-by-step explanation: