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10-1.Circle and System of Circles
easy
The equation of normal to the circle $2{x^2} + 2{y^2} - 2x - 5y + 3 = 0$ at $(1, 1)$ is
A
$2x + y = 3$
B
$x - 2y = 3$
C
$x + 2y = 3$
D
None of these
Solution
(c) The equation of tangent to the given circle at $(1,\,1)$ is
$2x + 2y – (x + 1) – $ $\frac{5}{2}\,(y + 1) + 3 = 0$
$ \Rightarrow $ $x – \frac{1}{2}\,y – \frac{1}{2} = 0$
$ \Rightarrow $$2x – y – 1 = 0$
Slope of tangent = $2$,
$\therefore $ Slope of normal $ = – \frac{1}{2}$
Hence equation of normal at $(1, 1)$ is
$y – 1 = – \frac{1}{2}(x – 1)$
$ \Rightarrow $ $x + 2y = 3.$
Standard 11
Mathematics
