If {x^2} + {y^2} + px + 3y - 5 = 0 and {x^2} + {y^2} + 5x + py + 7 = 0 cut orthogonally, then p is

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10-1.Circle and System of Circles

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If ${x^2} + {y^2} + px + 3y - 5 = 0$ and ${x^2} + {y^2} + 5x$ $ + py + 7 = 0$ cut orthogonally, then $p$ is

A

$\frac{1}{2}$

B

$1$

C

$\frac{3}{2}$

D

$2$

Solution

(a) $2{g_1}{g_2} + 2{f_1}{f_2} = {c_1} + {c_2}$ for orthogonal cut.

$ \Rightarrow p\,\,\left( {\frac{5}{2}} \right) + p\,\,\left( {\frac{3}{2}} \right) = – 5 + 7$

$\Rightarrow p = \frac{1}{2}$.

Standard 11

Mathematics

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