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10-1.Circle and System of Circles
normal
A line $lx + my + n = 0$ meets the circle ${x^2} + {y^2} = {a^2}$ at the points $P$ and $Q$. The tangents drawn at the points $P$ and $Q$ meet at $R$, then the coordinates of $R$ is
A
$\left( {\frac{{{a^2}l}}{n},\frac{{{a^2}m}}{n}} \right)$
B
$\left( {\frac{{ - {a^2}l}}{n},\frac{{ - {a^2}m}}{n}} \right)$
C
$\left( {\frac{{{a^2}n}}{l},\frac{{{a^2}n}}{m}} \right)$
D
None of these
Solution
(b) Suppose point be $(h, k)$.
Equation of common chord of contact is
$hx + ky – {a^2} = 0 \equiv lx + my + n = 0$
or $\frac{h}{l} = \frac{k}{m} = \frac{{ – {a^2}}}{n}$
or $h = \frac{{ – {a^2}l}}{n}$, $k = \frac{{ – {a^2}m}}{n}$.
Standard 11
Mathematics
