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  • The equation of the circle touching the line at the point

The equation of the circle touching the line \mathrm{2 x+3 y+1=0} at the point \mathrm{(1,-1)} and passing through the focus of the parabola \mathrm{y^{2}=4 x} is

Option: 1

\mathrm{3 x^{2}+3 y^{2}-8 x+3 y+5=0}


Option: 2

\mathrm{3 x^{2}+3 y^{2}+8 x-3 y+5=0}


Option: 3

\mathrm{x^{2}+y^{2}-3 x+y+6=0}


Option: 4

none of these


Answers (1)

best_answer

Equation of the circle is

\lambda(2 x+3 y+1)+(x-1)^{2}+(y+1)^{2}=0
It  passes through (1,0)\Rightarrow \lambda=\frac{-1}{3}

Equation of circle is \mathrm{3 x^{2}+3 y^{2}-8 x+3 y+5=0}

Hence (A) is the correct answer.

Posted by

Rakesh

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