jee-main 2019 Q69

jee-main · India · session2_09apr_shift1 Circles Circle-Related Locus Problems

If a tangent to the circle $x ^ { 2 } + y ^ { 2 } = 1$ intersects the coordinate axes at distinct points $P$ and $Q$, then the locus of the mid-point of $PQ$ is:
(1) $x ^ { 2 } + y ^ { 2 } - 16 x ^ { 2 } y ^ { 2 } = 0$
(2) $x ^ { 2 } + y ^ { 2 } - 4 x ^ { 2 } y ^ { 2 } = 0$
(3) $x ^ { 2 } + y ^ { 2 } - 2 x y = 0$
(4) $x ^ { 2 } + y ^ { 2 } - 2 x ^ { 2 } y ^ { 2 } = 0$

If a tangent to the circle $x ^ { 2 } + y ^ { 2 } = 1$ intersects the coordinate axes at distinct points $P$ and $Q$, then the locus of the mid-point of $PQ$ is:\\
(1) $x ^ { 2 } + y ^ { 2 } - 16 x ^ { 2 } y ^ { 2 } = 0$\\
(2) $x ^ { 2 } + y ^ { 2 } - 4 x ^ { 2 } y ^ { 2 } = 0$\\
(3) $x ^ { 2 } + y ^ { 2 } - 2 x y = 0$\\
(4) $x ^ { 2 } + y ^ { 2 } - 2 x ^ { 2 } y ^ { 2 } = 0$

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