A hyperbola passes through the point P212312 and has foci at 2 0 Then the tangent to this hyperbola at P also passes through the point JEE MAINS Mathematics 2017
The Eduladder is a community of students, teachers, and programmers just interested to make you pass any exams. So we solve previous year question papers for you.
See Our team
Wondering how we keep quality?
Got unsolved questions?

Ask Questions
Hey! Want to work with us? Our youtube channel See our Jd Want to apply? Do it today

Use Me  ?

New searches
Mathematics-2017-->View question


A hyperbola passes through the point P(2^(1/2),3^(1/2)) and has foci at (± 2, 0). Then the tangent to this hyperbola at P also passes through the point :-JEE MAINS-Mathematics-2017

(1) (-2^(1/2),-3^(1/2)) 
(2) 3x(2)^(1/2),2x3^(1/2)
(3) 2x2^(1/2),3x3^(1/2) 
(4) 3^(1/2),2^(1/2)


By:Purnima

Taged users:
|Aparna-Dasgupta

Likes:
Be first to like this question

Dislikes:
Be first to dislike this question

Talk about thisDelete|Like|Dislike|


Answers

Equation of hyperbola is 
(x^2/a^2)-(y^2/b^2) = 1
foci is (±2, 0) hence ae = 2, thus, a^2e^2 = 4
b2 = a2(e2 – 1)
 a^2 + b^2 = 4 ...(1)
Hyperbola passes through 2^(1/2), 3^(1/2)
 2/(a^2)-3/(b^2)=1...(2)
On solving (1) and (2)
a^2 = 8 (is rejected) and a^2 = 1 and b^2 = 3
(x^2)/1-(y^2)/3=1

Equation of tangent is (2^(1/2)x)/1-(3^(1/2)y)/3=1
Hence (2(2)^(1/2),3(3)^(1/2)) satisfy it.

leo

Likes:
Be first to like this answer

Dislikes:
Be first to dislike this answer
Talk about this|Once you have earned teacher badge you can edit this questionDelete|Like|Dislike|
------------------------------------

Can you help us to add better answer here? Please see this



Not the answer you're looking for? Browse other questions from this Question paper or ask your own question.

Join eduladder!