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If $x^2+y^2+p x+3 y-5=0$ and $x^2+y^2+5 x \quad+p y+7=0$ cut orthogonally, then $p$ is
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The correct answer is:
$\frac{1}{2}$
$2 g_1 g_2+2 f_1 f_2=c_1+c_2$ for orthogonal cut.
$\Rightarrow p\left(\frac{5}{2}\right)+p\left(\frac{3}{2}\right)=-5+7 \Rightarrow p=\frac{1}{2}$
$\Rightarrow p\left(\frac{5}{2}\right)+p\left(\frac{3}{2}\right)=-5+7 \Rightarrow p=\frac{1}{2}$
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