    Question

# A square has one vertex on the parabola y2=4ax and the diagonal through this vertex lies along the axis of the parabola. If the ends of the other diagonal lie on the parabola, the coordinate of one of the vertex of the square is

A
(0,2a)
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B
(4a,4a)
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C
(a,2a)
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D
none of these
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Solution

## The correct option is B (4a,4a)Let us suppose square will be ABCD,vertex A will be lie on origin,coordinates of A=(0,0)coordinates of B=(at2,2at)coordinates of C=(h,0). :- ( C will lie on x−axis. )coordinates of D=(at2,−2at) slope of AB =tan45∘=1. --(1) we know that slope of AB=y2−y1x2−x1put the value of x1,x2,y1,y2 from coordinates A & B,so, slope of AB=2at−0at2−0from equation 1, we know that,2at−0at2−0=12at=at2 and t=2if we consider the coordinated of B, than B=(at2,2at)put the value of ′t′B=(4a,4a)so, correct option will be 'B'  Suggest Corrections  0      Similar questions  Related Videos   Area under the Curve
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