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The circle passing through the point ( -...

The circle passing through the point `( -1,0)` and touching the y-axis at (0,2) also passes through the point.

A

`(-(3)/(2),0)`

B

`(-(5)/(2),2)`

C

`(-(3)/(2),(5)/(2))`

D

`(-4,0)`

Text Solution

Verified by Experts

The correct Answer is:
D
Equation of circle passing through a point `(x_(1), y_(2)) and touching the straight line L, is given by
`(x-x_(1))^(2)+(y-y_(1))^(2)+lambdaL=0`
`therefore` Equation of circle passing through (0,2) and touching x = 0`
`rArr (x-0)^(2)+(y-2)^(2)+lambdax=0" "...(i)`
Also, it passes through `(-1,0)rArr1+4-lambda=0`
`therefore lambda = 5`
Eq. (i) becomes,
`x^(2)+y^(2)-4y+4+5x=0`
`rArr x^(2)+y^(2)+5x-4y+4=0`,
For x-intercept put `y=0 rArrx^(2)+5x+4=0`,
`(x+1)(x+4)=0`
`thereforex = -1, -4`
Hence, (d) option (-4, 0).
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