If a circle C passing through (4, 0) touches | vedclass

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Question

Let $A$ be the center og given circle and $B$ be the center of circle $C$.

${x^2} + {y^2} + 4x - 6y - 1 = 0$

$	herefore A = \left( { - 2,3} i

Vedclass · Accepted Answer

$5$

Vedclass · Answer

Let $A$ be the center og given circle and $B$ be the center of circle $C$.

${x^2} + {y^2} + 4x - 6y - 1 = 0$

$	herefore A = \left( { - 2,3} ight)$ and $B = \left( {g,f} ight)$

Now, from the figure, we have 

$\frac{{ - 2 + g}}{2} = 1\,$ and $\frac{{3 + f}}{2} =  - 1$

                                                 (By mid point formula)

$ \Rightarrow g = 4\,$ and $f =  - 5$

Now, required radius

                           $ = OB = \sqrt {9 + 16}  = \sqrt {25}  = 5$

If a circle $C$ passing through $(4, 0)$ touches the circle $x^2 + y^2 + 4x - 6y - 12 = 0$ externally at a point $(1, -1),$ then the radius of the circle $C$ is

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