Question

A circle is concentric with the circle

$x ^ { 2 } + y ^ { 2 } - 6 x + 12 y + 15 = 0$ and has area double of its area. The equation of the circle is.

• A. $x ^ { 2 } + y ^ { 2 } - 6 x + 12 y - 15 = 0$
• B. $x ^ { 2 } + y ^ { 2 } - 6 x + 12 y + 15 = 0$
• C. $x ^ { 2 } + y ^ { 2 } - 6 x + 12 y + 45 = 0$
• D. None of these

Answer 1

Answer: (A)

$x ^ { 2 } + y ^ { 2 } - 6 x + 12 y - 15 = 0$

Answer 2

Equation of circle concentric to given circle is

$x ^ { 2 } + y ^ { 2 } - 6 x + 12 y + k = 0$ ….(i)

Radius of circle (i) $= \sqrt { 2 }$ (radius of given circle)

$\Rightarrow \sqrt { 9 + 36 - k } = \sqrt { 2 } \sqrt { 9 + 36 - 15 }$

$\Rightarrow 45 - k = 60 \Rightarrow k = - 15$

Hence the required equation of circle is

$x ^ { 2 } + y ^ { 2 } - 6 x + 12 y - 15 = 0$.