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The locus of the mid-point of the chord of contact of tangents

Question

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line $4 x - 5 y = 20$ to the circle $x^{2} + y^{2} = 9$ is : (A) $20 (x^{2} + y^{2}) - 36 + 45 y = 0$ (B) $20 (x^{2} + y^{2}) + 36 - 45 y = 0$ (C) $20 (x^{2} + y^{2}) - 20 x + 45 y = 0$ (D) $20 (x^{2} + y^{2}) + 20 x - 45 y = 0$

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Theodore Discussed

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line

4 x - 5 y = 20

to the circle

x^{2} + y^{2} = 9

is : (A)

20 (x^{2} + y^{2}) - 36 + 45 y = 0

(B)

20 (x^{2} + y^{2}) + 36 - 45 y = 0

(C)

20 (x^{2} + y^{2}) - 20 x + 45 y = 0

(D)

20 (x^{2} + y^{2}) + 20 x - 45 y = 0

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Question Text	The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line $4 x - 5 y = 20$ to the circle $x^{2} + y^{2} = 9$ is : (A) $20 (x^{2} + y^{2}) - 36 + 45 y = 0$ (B) $20 (x^{2} + y^{2}) + 36 - 45 y = 0$ (C) $20 (x^{2} + y^{2}) - 20 x + 45 y = 0$ (D) $20 (x^{2} + y^{2}) + 20 x - 45 y = 0$
Answer Type	Video solution: 1
Upvotes	150