JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Circle

Tangents are drawn from the point

(17, 7)

to the circle

x^{2} + y^{2} = 169

.

STATEMENT-1 : The tangents are mutually perpendicular.

because

STATEMENT-2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is

x^{2} + y^{2} = 338

(A)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1✓ Correct
(B)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C)Statement-1 is True, Statement-2 is False
(D)Statement-1 is False, Statement-2 is True

Answer: (A)

Solution

The circle

x^{2} + y^{2} = 169

has center

(0, 0)

and radius

r = 13

.

The director circle (locus of points from which perpendicular tangents can be drawn) has equation

x^{2} + y^{2} = 2 r^{2} = 2 (169) = 338

.

The point

(17, 7)

satisfies:

1 7^{2} + 7^{2} = 289 + 49 = 338

.

Since the point lies on the director circle, the tangents from it to the given circle are mutually perpendicular.

Both statements are true, and Statement-2 correctly explains Statement-1.

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Single correct option

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JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Circle

Solution

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