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  • I have a doubt, kindly clarify. - Co-ordinate geometry - JEE Main

 Two tangents are drawn from a point (-2, -1) to the curve, y2 = 4x.

If \alpha is the angle between them, then \left | tan\: \alpha \right | is equal    to:   

 

  • Option 1)

    \frac{1}{3}

  • Option 2)

    \frac{1}{\sqrt{3}}

  • Option 3)

    \sqrt{3}

  • Option 4)

    3

 

Answers (1)

As we learnt in

Common tangents of two circle -

When they intersect, there are two common tangents, both of them being direct.

- wherein

 

 

The locus of point of intersection of tangents to the parabola y^{2}=4ax inclined at an angle \alpha to each other is

tan^{2}\alpha\left ( x+a \right ) ^{2}=y^{2}-4ax

Also, y^{2}=4x;\:So,\:a=1

Point of intersection is (-2,-1)

Thus,

tan^{2}\alpha \left ( -2+1 \right )=\left ( -1 \right )^{2}-4\left ( -2 \right )

tan^{2}\alpha =9

\left | tan\alpha \right |=3

 

 

  

 


Option 1)

\frac{1}{3}

This option is incorrect.

Option 2)

\frac{1}{\sqrt{3}}

This option is incorrect.

Option 3)

\sqrt{3}

This option is incorrect.

Option 4)

3

This option is correct.

Posted by

Vakul

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