The locus of a point P(\alpha ,\beta ) moving under the condition that the line y=\alpha x+\beta is a tangent to the hyperbola \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1   is

  • Option 1)

    a circle

  • Option 2)

    an ellipse

  • Option 3)

    a hyperbola

  • Option 4)

    a parabola.

 

Answers (1)
V Vakul

As we learnt in 

Condition for Tangency in Hyperbola -

C^{2}= a^{2}m^{2}-b^{2}

- wherein

For the Hyperbola

\frac{x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}= 1

 

y = \alpha x + \beta is tangent to  \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1  

Condition for tangency for y = mn + C is C2= a2m2 - b2

i.e. \beta^{2}=a^{2}\alpha^{2}-b^{2}

Thus replace (\alpha , \beta ) by (x, y)

y2 = a2x2 - b2 which is hyperbola.  


Option 1)

a circle

this is incorrect option

Option 2)

an ellipse

this is incorrect option

Option 3)

a hyperbola

this is correct option

Option 4)

a parabola.

this is incorrect option

Preparation Products

JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Knockout JEE Main April 2021 (Subscription)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
Buy Now
Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Knockout JEE Main January 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Exams
Articles
Questions