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Question

# The auxiliary circle of x29+y24=1 touches a parabola having axis of symmetry as y−axis at its vertex . If the latus rectum of parabola is equal to radius of director circle of auxiliary circle, then the equation of parabola can be

A
x2=18(y3)
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B
x2=16(y+3)
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C
x2=16(y3)
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D
x2=18(y+3)
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Solution

## The correct option is D x2=−√18(y+3)Auxiliary circle of ellipse is x2+y2=9 Director circle equatio for auxilary circle is x2+y2=18⇒(r=√18) So, length of latus rectum =√18 and vertex of parabola is (±3,0) as parabola touches the circle at vertex only So. equation of parabola is (x−0)2=±√18(y±3) therefore equation of upward parabola will be x2=√18(y−3) And, equation of downward parabola will be x2=−√18(y+3)

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