Equation of circle which touches axes of coordinates and line frac{x}{3} + frac{y}{4} = 1 and whose

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10-1.Circle and System of Circles

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The equation of circle which touches the axes of coordinates and the line $\frac{x}{3} + \frac{y}{4} = 1$ and whose centre lies in the first quadrant is ${x^2} + {y^2} - 2cx - 2cy + {c^2} = 0$, where $c$ is

A

$1$

B

$2$

C

$3$

D

$6$

Solution

(d) Its centre is of type $(c, c)$ and

radius is $\left| {\frac{{4c + 3c – 12}}{5}} \right|\;$

$= \sqrt {{c^2}} $

$\Rightarrow c = 6$.

Standard 11

Mathematics

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