IIT-JEE 2007 · Paper 1 · Mathematics Q55

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MathematicsAssertion and reason+3 / -1Question 55 of 66

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 $x^2+y^2=338$ .

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

Statement-1 is True, Statement-2 is False

Statement-1 is False, Statement-2 is True

Answer and worked solution

Official answer: A

Director circle. Perpendicular tangents to $x^2+y^2=a^2$ meet on $x^2+y^2=2a^2=338$ . Statement 2 is True.

The point. $17^2+7^2=289+49=338$ : $(17,7)$ lies on the director circle, so its tangents are perpendicular. Statement 1 is True, and Statement 2 explains it.

(A)

Topics:Tangents and normals

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IIT-JEE 2007 · Paper 1, Mathematics question 55