Question

The equations of three circles are

$3 x ^ { 2 } + 3 y ^ { 2 } - 36 x + 81 = 0$ and $x ^ { 2 } + y ^ { 2 } - 16 x + 81 = 0$The coordinates of the point from which the length of tangents drawn to each of the three circles is equal

• A. $\left( \frac { 33 } { 4 } , 2 \right)$
• B. (2, 2)
• C. $\left( 2 , \frac { 33 } { 4 } \right)$
• D. None

Answer 1

Answer: (D)

None

Answer 2

The required point is the radical centre of the three given circles

Now, $S _ { 1 } - S _ { 2 } = 0 \Rightarrow - 16 y + 37 = 0$,

$S _ { 2 } - S _ { 3 } = 0 \Rightarrow 4 x - 54 = 0$and $S _ { 3 } - S _ { 1 } = 0 \Rightarrow - 4 x + 16 y + 17 = 0$

Solving these equations, we get

.

Hence the required point is $\left( \frac { 27 } { 2 } , \frac { 37 } { 16 } \right)$