Question

The equation of the circle, which passes through the point (2a, 0) and whose radical axis is $x = \frac { a } { 2 }$ with respect to the circle $x ^ { 2 } + y ^ { 2 } = a ^ { 2 }$ , will be

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

Answer 1

Answer: (A)

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

Answer 2

Equation of radical axis is $x = \frac { a } { 2 }$ $\Rightarrow \quad 2 x - a = 0$

Equation of required circle is $x ^ { 2 } + y ^ { 2 } - a ^ { 2 } + \lambda ( 2 x - a ) = 0$

$\bullet \bullet$ It is passes through the point (2a, 0) ,

$\therefore$ $4 a ^ { 2 } - a ^ { 2 } + \lambda ( 4 a - a ) = 0$

$\therefore$ Equation of circle is $x ^ { 2 } + y ^ { 2 } - a ^ { 2 } - 2 a x + a ^ { 2 } = 0$

$\Rightarrow x ^ { 2 } + y ^ { 2 } - 2 a x = 0$