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(A) For the circle $x^2 + y^2 = r^2$,the locus of points from which perpendicular tangents can be drawn is the director circle $x^2 + y^2 = 2r^2$.Here

Vedclass · Accepted Answer

Statement-$1$ is true,Statement-$2$ is true. Statement-$2$ is the correct explanation for Statement-$1$.

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(A) For the circle $x^2 + y^2 = r^2$,the locus of points from which perpendicular tangents can be drawn is the director circle $x^2 + y^2 = 2r^2$.Here,$r^2 = 169$,so the director circle is $x^2 + y^2 = 2(169) = 338$.For Statement-$1$: Check if $(17, 7)$ lies on $x^2 + y^2 = 338$. $17^2 + 7^2 = 289 + 49 = 338$. Since it satisfies the equation,the tangents are perpendicular. Statement-$1$ is true.For Statement-$2$: By definition,the director circle is the locus of points from which perpendicular tangents are drawn to the circle. Thus,every point on $x^2 + y^2 = 338$ allows for perpendicular tangents to $x^2 + y^2 = 169$. Statement-$2$ is true and explains Statement-$1$.

Tangents are drawn from the point $(17, 7)$ to the circle $x^2 + y^2 = 169$.
Statement-$1$: These tangents are perpendicular to each other.
Statement-$2$: From every point on the circle $x^2 + y^2 = 338$,perpendicular tangents can be drawn to the given circle.

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Tangents are drawn from the point $(17, 7)$ to the circle $x^2 + y^2 = 169$.Statement-$1$: These tangents are perpendicular to each other.Statement-$2$: From every point on the circle $x^2 + y^2 = 338$,perpendicular tangents can be drawn to the given circle.