Question

Equation of the circle which touches the lines $x = 0 , y = 0$ and $3 x + 4 y = 4$ is.

• A. $x ^ { 2 } - 4 x + y ^ { 2 } + 4 y + 4 = 0$
• B. $x ^ { 2 } - 4 x + y ^ { 2 } - 4 y + 4 = 0$
• C. $x ^ { 2 } + 4 x + y ^ { 2 } + 4 y + 4 = 0$
• D. $x ^ { 2 } + 4 x + y ^ { 2 } - 4 y + 4 = 0$

Answer 1

Answer: (B)

$x ^ { 2 } - 4 x + y ^ { 2 } - 4 y + 4 = 0$

Answer 2

Let centre of circle be (h, k). Since it touches both axes, therefore $h = k = a$

Hence equation can be $( x - a ) ^ { 2 } + ( y - a ) ^ { 2 } = a ^ { 2 }$

But it also touches the line $3 x + 4 y = 4$.

Therefore, $\frac { 3 a + 4 a - 4 } { 5 } = a \Rightarrow a = 2$

Hence the required equation of circle is

$x ^ { 2 } + y ^ { 2 } - 4 x - 4 y + 4 = 0$ .