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Standard IX

Mathematics

RHS Criteria for Congruency

P x1,y1 and ...

Question

$P (x_{1}, y_{1})$ and $Q (x_{2}, y_{2})$ and $O$ is the origin , the length of common chord of circles drawn on $O P$ and $O Q$ as diameter is

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Solution

$e q^{n}$ of circle $- 1 = S_{1} : - x^{2} + y^{2} - x x_{1} - y y_{1} = 0$
$e q^{n}$ of circle $- 2 = S_{2} = x^{2} + y^{2} - x x_{2} - y y_{2} = 0$
$∴ e q^{n}$ of common chord is $S_{1} - S_{2} = 0$
$∴ x (x_{2} - x_{1}) + y (y_{2} - y_{1}) = 0$
is $e q^{n}$ of common chord.

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P(x1,y1) and Q(x2,y2) and O is the origin , the length of common chord of circles drawn on OP and OQ as diameter is

eqn of circle −1=S1:−x2+y2−xx1−yy1=0eqn of circle −2=S2=x2+y2−xx2−yy2=0∴eqn of common chord is S1−S2=0∴x(x2−x1)+y(y2−y1)=0is eqn of common chord.

$P (x_{1}, y_{1})$ and $Q (x_{2}, y_{2})$ and $O$ is the origin , the length of common chord of circles drawn on $O P$ and $O Q$ as diameter is

$e q^{n}$ of circle $- 1 = S_{1} : - x^{2} + y^{2} - x x_{1} - y y_{1} = 0$
$e q^{n}$ of circle $- 2 = S_{2} = x^{2} + y^{2} - x x_{2} - y y_{2} = 0$
$∴ e q^{n}$ of common chord is $S_{1} - S_{2} = 0$
$∴ x (x_{2} - x_{1}) + y (y_{2} - y_{1}) = 0$
is $e q^{n}$ of common chord.