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 $x^{2} + y^{2} = 338$ . [2007]

Question

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 $x^{2} + y^{2} = 338$ . [2007]

Smart Achievers · Accepted Answer

(1)

Equation of director circle of the given circle $x^{2} + y^{2} = 169$ is $x^{2} + y^{2} = 2 \times 169 = 338$

We know that from every point on the director circle, the tangents drawn to the given circle are perpendicular to each other.

Since (17,7) lies on the director circle,

$∴$ The tangents from (17,7) to the given circle are mutually perpendicular.

Solution

Q.
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 $x^{2} + y^{2} = 338$ . [2007]

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

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

3 Statement-1 is True, Statement-2 is False.

4 Statement-1 is False, Statement-2 is True.

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