Q.

The tangents drawn from the origin to the circle x2+y2- 2px–2qy+q2=0 are perpendicular if

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a

p2+q2=1

b

p2-q2=1

c

p2-q2=0

d

none of these

answer is C.

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Detailed Solution

Equation of the given circle can be written as       (x−p)2+(y−q)2=p2                      (i)This has (p, q) as the centre and p as the radius showing that it touches y-axis. So one of the tangents from the origin to the circle is y-axis.⇒     Other tangent from the origin to the circle must be x-axis. which is possible if q = ± p.⇒   p2−q2=0.
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