The equation of the tangent to the circle x2+y2+4x-4y+4=0 which make equal intercepts on the positive coordinate axes is:

Question

The equation of the tangent to the circle x2+y2+4x-4y+4=0 which make equal intercepts on the positive coordinate axes is: (A)  x+y=2  (B)  x+y=2√2  (C)  x+y=4  (D)  x+y=8

Tardigrade Admin · Accepted Answer

Let the equation of the required tangent be x+y=a then, length of the perpendicular from centre = radius | (-2+2-a/√2) |=2 ⇒ a=2√2 Hence, the equation of tangent is x+y=2√2

Q. The equation of the tangent to the circle $x^{2} + y^{2} + 4 x - 4 y + 4 = 0$ which make equal intercepts on the positive coordinate axes is:

$x + y = 2$

$x + y = 22$

$x + y = 4$

$x + y = 8$

Let the equation of the required tangent be $x + y = a$ then, length of the perpendicular from centre = radius $∣ ∣ \frac{- 2 + 2 - a}{2} ∣ ∣ = 2$ $\Rightarrow$ $a = 22$ Hence, the equation of tangent is $x + y = 22$

Q. The equation of the tangent to the circle x2+y2+4x−4y+4=0 which make equal intercepts on the positive coordinate axes is:

x+y=2

x+y=22​

x+y=4

x+y=8