# If a circle passing through the point (-1, 0) touches y-axis at (0, 2), then the length of the chord of the circle along the x-axis is : Option 1) Option 2) Option 3) 3 Option 4) 5

As learnt in concept

Circle touching y-axis and having radius r -

$x^{2}+y^{2}+ 2gx\pm 2ry+g^{2}= 0$

- wherein

Where g is a variable parameter.

Equation of a circle -

$\left ( x-h \right )^{2}+\left ( y-k \right )^{2}= r^{2}$

- wherein

Circle with centre $\left ( h,k \right )$ and radius $r$.

If the centre is (h, 2) then

equartion of circle is

$\left ( x-h \right )^{2}+\left ( y-2 \right )^{2}=h^{2}$

and it passes through point (-1, 0)

putting values , we get

$h=\frac{-5}{2}$

So centre is

$\left ( \frac{-5}{2}, 2 \right )$

$equation \: \left ( x+\frac{5}{2} \right )^{2}+\left ( y-2 \right )^{2}$$=\left ( \frac{5}{2} \right )^{2}$

(-4, 0) satisfies this equation.

Option 1)

Option 2)

Option 3)

3

Option 4)

5

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