Question

The equation of the tangent to the circle $x^2+y^2$ + 2x + 2y - 7 = 0 which makes ${45}^{\circ }$ with the x axis is

• A. y = x + 1
• B. y = x
• C. y = x 3
• D. y = x + 3

Answer 1

The correct option is C y = x 3

For the circle $x^2+y^2$ + 2x + 2y - 7 = 0, centre (-1, -1), radius = $\sqrt{1+1+7}$ = 3
Equation of the line having indination ${45}^{\circ }$ is x - y + k = 0
x + y + k = 0 is a tangent to the circle $\Rightarrow$ $\frac{|-1+1+k|}{\sqrt{2}}$ = 3 $\Rightarrow$ $\left|k\right|$ = 3$\sqrt{2}$ $\Rightarrow$ k = $\pm$ 3$\sqrt{2}$
$\therefore$ Required tangent is x - y $\pm$ 3$\sqrt{2}$ = 0 $\Rightarrow$ y = x $\pm$ 3$\sqrt{2}$