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Question

Equation of the parabola with its vertex at (1,1) and focus (3,1) is


A

(x-1)2=8(y1)

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B

(y-1)2=8(x3)

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C

(y-1)2=8(x1)

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D

(x-3)2=8(y1)

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Solution

The correct option is C

(y-1)2=8(x1)


Finding the equation of a parabola.

The vertex of parabola (h,k)=(1,1)

and its focus (a+h,k)=(3,1)

a+h=3

a=2

the y-coordinates of vertex of parabola and focus are equal,

the axis of the parabola is parallel to the x-axis.

The equation of the parabola is (yk)2=4a(xh)

(y1)2=4×2(x1)

(y1)2=8(x1)

Hence, Option ‘C’ is Correct.


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