If the chord of contact of P(x_1, y_1) with r | vedclass

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(B) The equation of the chord of contact of $P(x_1, y_1)$ with respect to the circle $x^2+y^2=a^2$ is given by $xx_1 + yy_1 = a^2$. Let the circle be

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$2a^2$

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(B) The equation of the chord of contact of $P(x_1, y_1)$ with respect to the circle $x^2+y^2=a^2$ is given by $xx_1 + yy_1 = a^2$. Let the circle be $S: x^2+y^2-a^2=0$. The equation of the pair of tangents from $P$ to the circle is $SS_1 = T^2$,where $S_1 = x_1^2+y_1^2-a^2$ and $T = xx_1+yy_1-a^2$. This simplifies to $(x^2+y^2-a^2)(x_1^2+y_1^2-a^2) = (xx_1+yy_1-a^2)^2$. Since $\angle AOB = 90^{\circ}$,the lines $OA$ and $OB$ are perpendicular. For a circle $x^2+y^2+2gx+2fy+c=0$,the condition for perpendicular lines at the origin is $coeff(x^2) + coeff(y^2) = 0$. Expanding the equation: $(x^2+y^2-a^2)(x_1^2+y_1^2-a^2) = x^2x_1^2 + y^2y_1^2 + a^4 + 2xxy_1y - 2x^2x_1a^2 - 2yy_1a^2$. Sum of coefficients of $x^2$ and $y^2$ is $(x_1^2+y_1^2-a^2) - x_1^2 + (x_1^2+y_1^2-a^2) - y_1^2 = 0$. $x_1^2+y_1^2-a^2-x_1^2 + x_1^2+y_1^2-a^2-y_1^2 = 0$. $x_1^2+y_1^2-2a^2 = 0$,which gives $x_1^2+y_1^2 = 2a^2$.

If the chord of contact of $P(x_1, y_1)$ with respect to the circle $x^2+y^2=a^2$ meets the circle at $A$ and $B$; and if $\angle AOB=90^{\circ}$,then $x_1^2+y_1^2=$

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