If a circle C passing through the point (4, 0 | vedclass

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Question

Tangent at $\left( {1, - 1} \right)$ is $x\left( 1 \right) + y\left( { - 1} \right) + 2\left( {x + 1} \right) - 3\left( {y - 1} \right) - 12

Vedclass · Accepted Answer

$5$

Vedclass · Answer

Tangent at $\left( {1, - 1} \right)$ is $x\left( 1 \right) + y\left( { - 1} \right) + 2\left( {x + 1} \right) - 3\left( {y - 1} \right) - 12 = 0$

$ = 3x - 4y = 7$

required circle is ${\left( {x + 1} \right)^2} + {\left( {y - 1} \right)^2} + \lambda \left( {3x - 4y - 7} \right) = 0$

It pass through $\left( {4,0} \right)$

$ \Rightarrow 9 + 1 + \lambda \left( {12 - 7} \right) = 0 \Rightarrow  =  - 2$

$ \Rightarrow $ required circleb is ${x^2} + {y^2} - 8x + 10y + 16 = 0$

$ \Rightarrow $ Radius $ = \sqrt {16 + 25 - 16}  = 5$

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

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