Tangents are drawn from the point (17,7) to t | vedclass

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(A) The equation of the circle is $x^2+y^2=169$,which is of the form $x^2+y^2=r^2$ with $r=13$.The director circle of a circle $x^2+y^2=r^2$ is the lo

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

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(A) The equation of the circle is $x^2+y^2=169$,which is of the form $x^2+y^2=r^2$ with $r=13$.The director circle of a circle $x^2+y^2=r^2$ is the locus of points from which mutually perpendicular tangents can be drawn to the circle,given by $x^2+y^2=2r^2$.For the given circle,$r^2=169$,so the director circle is $x^2+y^2=2(169) = 338$.Thus,$Statement-2$ is True.Now,check if the point $(17,7)$ lies on the director circle $x^2+y^2=338$:$17^2 + 7^2 = 289 + 49 = 338$.Since the point $(17,7)$ satisfies the equation of the director circle,the tangents drawn from this point to the circle are mutually perpendicular.Thus,$Statement-1$ is True and $Statement-2$ is the correct explanation for $Statement-1$.

Tangents are drawn from the point $(17,7)$ to the circle $x^2+y^2=169$.
$STATEMENT-1$: The tangents are mutually perpendicular.
$STATEMENT-2$: The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is $x^2+y^2=338$.

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Tangents are drawn from the point $(17,7)$ to the circle $x^2+y^2=169$.$STATEMENT-1$: The tangents are mutually perpendicular.$STATEMENT-2$: The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is $x^2+y^2=338$.