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10-1.Circle and System of Circles
medium
The gradient of the radical axis of the circles ${x^2} + {y^2} - 3x - 4y + 5 = 0$ and $3{x^2} + 3{y^2} - 7x + 8y + 11 = 0$ is
A
$\frac{1}{3}$
B
$ - \frac{1}{{10}}$
C
$ - \frac{1}{2}$
D
$ - \frac{2}{3}$
Solution
(b) Equation of radical axis is $S_1 -S_2 = 0$
${S_1} \equiv {x^2} + {y^2} – 3x – 4y + 5 = 0$
${S_2} \equiv {x^2} + {y^2} – \frac{7}{3}x + \frac{{8y}}{3} + \frac{{11}}{3} = 0$
$\therefore$ Radical axis is $ – 2x – 20y – 4 = 0$
Hence gradient of radical axis $ = – \frac{1}{{10}}$.
Standard 11
Mathematics
