Question

The equation of the tangent to the circle $x^2+y^2+4x-4y+4=0$ which makes equal intercepts on the positive coordinates axes, is

• A. $x+y=2$
• B. $x+y=2\sqrt{2}$
• C. $x+y=4$
• D. $x+y=8$

Answer 1

The correct option is B

$x+y=2\sqrt{2}$

Find the equation of the tangent based on given information

Given, equation of circle $x^2+y^2+4x-4y+4=0....\left(\mathrm{i}\right)$

So, the centre is at $(-2,2)$
Radius $r=\sqrt{4+4-4}$

$r=2$

Now, given tangent to equation $\left(\mathrm{i}\right)$ makes equal intercepts on the coordinate axes,
So, let the equation of tangent be $x+y=a$

Now since, length of tangent from the centre $=$ Radius

$$\begin{gathered} \Rightarrow \frac{|-2+2-a\mid }{\sqrt{2}}=2 \\ \Rightarrow a=2\sqrt{2} \end{gathered}$$

Therefore, the equation of the required tangent is $x+y=2\sqrt{2}$
Hence, the option $\left(b\right)$ is correct.