If a circle C, whose radius is 3, touch | vedclass

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Question

Given circle is:

${x^2} + {y^2} + 2x - 4y - 4 = 0$

$	herefore $ it center is $\left( { - 1,2} ight)$ and radius is $3$ units.

Let $A=

Vedclass · Accepted Answer

$2\sqrt 5$

Vedclass · Answer

Given circle is:

${x^2} + {y^2} + 2x - 4y - 4 = 0$

$	herefore $ it center is $\left( { - 1,2} ight)$ and radius is $3$ units.

Let $A=(x,y)$ be the center of the circle $C$ 

$	herefore \frac{{x - 1}}{2} = 2 \Rightarrow x = 5$

$ \Rightarrow y = 2$

So the center of $C$ is $(5,2)$ and its radius is $3$

$	herefore $ equation of center $C$ is:

${x^2} + {y^2} - 10x - 4y + 20 = 0$

$	herefore $ The length of the intercept it cuts on the $X$-axis

$ = 2\sqrt {{g^2} - c}  = 2\sqrt {25 - 20}  = 2\sqrt 5 $

If a circle $C,$ whose radius is $3,$ touches externally the circle, $x^2 + y^2 + 2x - 4y - 4 = 0$ at the point $(2, 2),$ then the length of the intercept cut by circle $c,$ on the $x-$ axis is equal to

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