Question

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

Answer 1

Answer: (C)

$y = x \pm 6 \sqrt { 2 }$

Answer 2

$y = m x + c$ is a tangent, if $c = \pm a \sqrt { 1 + m ^ { 2 } }$, where

$m = \tan 45 ^ { \circ } = 1$

The equation is $y = x \pm 6 \sqrt { 2 }$.