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The equation of the circle, which touche...

The equation of the circle, which touches the parabola `y^2=4x` at (1,2) and passes through the origin is :

A

`(5)/(2)`

B

`(5)/(2sqrt2)`

C

`(5)/(sqrt2)`

D

`5sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
C
The equation of the tangent at `(1, 2)` to `y^(2)=4x` is `x-y+1=0`. Let the equation of the required circle be `(x-1)^(2)+(4-2)^(2)+l(x-y)+1=0` it also passes through `(0, 0)`
`rArr" "l=-5`
`"Equation of required circle is "^(2)+y^(2)-7x+y=0`
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