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Q)

Find the equation of the parabola if the vertex is 4,1 one with the focus i

Find the equation of the parabola if the vertex is 4,1 one with the focus is 4, -3

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A)

Equation of a parabola given the vertex and focus is:
(x – h)^2 = 4p(y – k)

The vertex (h, k) is 4, 1
The distance is p, and since the y coordinates of 1 are equal, the distance is 4- 4 = 0.
So p = 0

Our parabola equation becomes:
(x - 4)^2 = 4(0)(y - 1)
(x - 4)^2 =0

 

X^2-8x+16=0 is the equation

 

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