Write the length of the intercept made by the circle `x^2+y^2+2x-4y-5=0` on y-axis.

Options

A. `6`
B. `sqrt8`
C. `9`
D. `2 sqrt(14)`

Answer

`2 sqrt(14)`

Explanation

For finding the points on` y` axis, where the circle above intersects

we substitute `x` as `0` .

We thus get `y^(2)-6 y-5=0`


`Rightarrow(y)`=`frac(6 pm sqrt(36+20))(2)`=`frac(6 pm sqrt(56))(2)`

`Rightarrow (y)`=`3 pm sqrt(14)`


So, the circle intersects the `y`axis at points `(0,3-sqrt(14))` and `(0,3+sqrt(14))`.

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