Q.

The tangent at any point to the circle x2+y2=r2  meets the coordinate axes at A and B. If the lines drawn parallel to the coordinate axes through A & B intersect at P. Then the locus of P is

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a

x2+y2=r−2

b

x−2+y−2=r2

c

x−2+y−2=r−2

d

x−2−y−2=r−2

answer is C.

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Detailed Solution

Equation of tangent at R(rcos⁡θ,rsin⁡θ) is xcos⁡θ+ysin⁡θ=r −−−−(1)Arcosθ,0,B0,rsinθ Let P(h,k) then h=rcos⁡θ,k=rsin⁡θcos⁡θ=rh,sin⁡θ=rk∴1=r21h2+1k2 Required locus x−2+y−2=r−2
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The tangent at any point to the circle x2+y2=r2  meets the coordinate axes at A and B. If the lines drawn parallel to the coordinate axes through A & B intersect at P. Then the locus of P is