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  • The equation of the common tangent touching the circle and the parabola <im

The equation of the common tangent touching the circle (x-3)^2+y^2=9 and the parabola
y^2=4 x below the x–axis is

Option: 1

\sqrt{3} y=3 x+1


Option: 2

\sqrt{3} y=-(x+3)


Option: 3

\sqrt{3} y=x+3


Option: 4

\sqrt{3} y=-(3 x+1)


Answers (1)

best_answer

Equation of tangent at (x1, y1) on the parabola y^2=4 x is 

2 x-y_1+2 x_1=0

length of perpendicular from centre of the circle (x-3)^2+y^2=9 is 

\frac{6+2 x_1}{\sqrt{4+y_1^2}}=3 \quad \Rightarrow x_1=0,3 \& y_1=0, \pm 2 \sqrt{3}

Hence required equation \sqrt{3} y=-(x+3)

 

Posted by

Kuldeep Maurya

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