Tangents are drawn from a point P to the parabola y2=4ax. If the chord of contact of the parabola is a tangent to the hyperbola x2a2−y2b2=1, then the locus of P is
A
a2x2=a4−y2b2
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B
4a2x2=4a4−y2b2
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C
4a2x2=a4−y2b2
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D
a2x2=4a4−y2b2
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Solution
The correct option is B4a2x2=4a4−y2b2 Let the coordiates of point P be (h,k)
then the equation of the chord of contact of the parabola is yk=2a(x+h) ⇒y=2akx+2ahk⋯(1)
Since equation (1) is a tangent to the hyperbola, x2a2−y2b2=1
So, c2=a2m2−b2⇒(2ahk)2=a2(2ak)2−b2⇒4a2h2=4a4−k2b2