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)

    \frac{3}{2}

  • Option 2)

    \frac{5}{2}

  • Option 3)

    3

  • Option 4)

    5

 

Answers (1)

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

radius = |h|

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)

\frac{3}{2}

Option 2)

\frac{5}{2}

Option 3)

3

Option 4)

5

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