Equations of tangents to circle {x^2} + {y^2} = 36 which are inclined at an angle of {45^o} to x -ax

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10-1.Circle and System of Circles

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The equations of the tangents to the circle ${x^2} + {y^2} = 36$ which are inclined at an angle of ${45^o}$ to the $x$-axis are

A

$x + y = \pm \sqrt 6 $

B

$x = y \pm 3\sqrt 2 $

C

$y = x \pm 6\sqrt 2 $

D

None of these

Solution

(c) $y = mx + c$ is a tangent, if $c = \pm a\sqrt {1 + {m^2}} $, where $m = \tan {45^o} = 1$

$\therefore \;$The equation is $y = x \pm 6\sqrt 2 $.

Standard 11

Mathematics

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