Question

The gradient of the radical axis of the circles $x ^ { 2 } + y ^ { 2 } - 3 x - 4 y + 5 = 0$ and $3 x ^ { 2 } + 3 y ^ { 2 } - 7 x + 8 y + 11 = 0$ is

• A. $\frac { 1 } { 3 }$
• B. $- \frac { 1 } { 10 }$
• C. $- \frac { 1 } { 2 }$
• D. $- \frac { 2 } { 3 }$

Answer 1

Answer: (B)

$- \frac { 1 } { 10 }$

Answer 2

Equation of radical axis is $S _ { 1 } - S _ { 2 } = 0$

$S _ { 1 } \equiv x ^ { 2 } + y ^ { 2 } - 3 x - 4 y + 5 = 0$, $S _ { 2 } \equiv x ^ { 2 } + y ^ { 2 } - \frac { 7 } { 3 } x + \frac { 8 y } { 3 } + \frac { 11 } { 3 } = 0$

$\therefore$ Radical axis is $- 2 x - 20 y + 4 = 0$.

Hence, gradient of radical axis = $- \frac { 1 } { 10 }$