Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard
  1. Home
  2. Engineering
  3. Try this! - Co-ordinate geometry - JEE Main-6
# Engineering

If the tangent to the parabola  y^{2}=x  at a point  (\alpha,\beta),(\beta>0)  is also a tangent to the ellipse x^{2}+2y^{2}=1 , then  \alpha is equal to :

  • Option 1)

    \sqrt{2}-1

  • Option 2)

    2\sqrt{2}-1

     

  • Option 3)

    2\sqrt{2}+1

  • Option 4)

    \sqrt{2} +1

 

Answers (1)
V Vakul

y^{2}=x

since (\alpha,\beta)   lies on parabola

\\\beta^{2}=\alpha\\\\\:(\alpha,\beta)=(\beta^{2},\beta)\\\\\:tangent\:\:to\:\:parabola\\\\\:y.\beta=\frac{1}{2}\left ( x+\beta^{2} \right )\\\\\:y=\frac{x}{2\beta}+\frac{\beta}{2}

tangent to parabola is also tangent to ellipse

\\\frac{x^{2}}{4}=1.\left ( \frac{1}{4\beta} \right )+\frac{1}{2}\\\\\:\beta^{2}=\sqrt{2}+1,\alpha=\sqrt{2}+1

 


Option 1)

\sqrt{2}-1

Option 2)

2\sqrt{2}-1

 

Option 3)

2\sqrt{2}+1

Option 4)

\sqrt{2} +1

Similar Questions

Latest Asked Questions

Most Viewed Questions

Preparation Products

Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Test Series JEE Main 2024

Chapter/Subject/Full Mock Tests for JEE Main, Personalized Performance Report, Weakness Sheet, Complete Answer Key,.

₹ 7999/- ₹ 4999/-
Buy Now
JEE Main Rank Booster 2023

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, Faculty Support.

₹ 9999/- ₹ 6999/-
Buy Now
Knockout JEE Main (One Month Subscription)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, Faculty Support.

₹ 7999/- ₹ 4999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
Start Now
 
Exams
Articles
Questions