Question

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

• A. x + y = 2
• B. x + y =
• C. x + y = 2
• D. none

Answer 1

The correct option is C x + y = 2

For the circle $x^2+y^2$ + 4x - 4y + 4 = 0, centre is (-2, 2), radius = $\sqrt{4+4-4}$ = 2
Equation of a line having equal intercepts on the positive axes is x + y + k = 0,
k $<$ 0 x + y + k = 0, k $<$ 0 is a tangent to the circle $\Rightarrow$ $\frac{|-2+2+k|}{\sqrt{2}}$ = 2 $\Rightarrow$ k = $\pm$2$\sqrt{2}$ $\Rightarrow$ k = - 2 $\sqrt{2}$
($\because$ k $<$ 0)
$\therefore$ Required tangent equation is x + y - 2$\sqrt{2}$ = 0