If two tangents drawn from a point P to the parabola y^{2}=4x are at right angles, then the locus of P is

  • Option 1)

    x=1

  • Option 2)

    2x+1=0

  • Option 3)

    x=-1

  • Option 4)

    2x-1=0

 

Answers (1)
P Plabita

As we learnt in

Equation of tangent -

yy_{1}= 2a\left ( x+x_{1} \right )

 

- wherein

Tangent at  P\left ( x,y_{1} \right )on  y^{2}=4ax

 

 and

Standard equation of parabola -

y^{2}=4ax

- wherein

 

Locus of perpendicular tangents is the directrix.

so, x = -a

i.e. x = -1 


Option 1)

x=1

This option is incorrect.

Option 2)

2x+1=0

This option is incorrect.

Option 3)

x=-1

This option is correct.

Option 4)

2x-1=0

This option is incorrect.

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