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  • The equation of circle touching the parabola <img alt="\mathrm

The equation of circle touching the parabola \mathrm{y^2 = 4x} at the point (1, −2) and passing through origin is 

 

Option: 1

\mathrm{x^2+y^2+6 x+9 y=0}


Option: 2

\mathrm{x^2+y^2-3 x-4 y=0}


Option: 3

\mathrm{x^2+y^2-7 x-y=0}


Option: 4

\mathrm{x^2+y^2-9 x-2 y=0}


Answers (1)

Tangent to parabola at (1,-2) will be \mathrm{ x+y+1=0}, equation of circle touching the parabola at (1,-2) will be\mathrm{ (x-1)^2+(y+2)^2+\lambda(x+y+1)=0}, it passes through origin. So \mathrm{ \lambda=-5.} Hence equation of circle will be\mathrm{ x^2+y^2-7 x-y=0..}
Hence answer is (c).

Posted by

Sumit Saini

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