0

Guest

Courses New

I want to request the solution for question no. 12. I tried solving it by finding the equation of normal at parametric point P and putting y= 0 but didn't get the answer. What's wrong with it?

I want to request the solution for question no. 12. I tried solving it by finding the equation of normal at parametric point P and putting y= 0 but didn't get the answer. What's wrong with it?

Question Image
Grade:11

1 Answers

Samyak Jain
333 Points
5 years ago
Let coordinates of point P on the hyperbola be (a sec\large \Theta, b tan\large \Theta).
\thereforeΒ the coordinates of the foot of perpendicular N are (a sec\large \Theta, 0).
Differentiate the equation of the hyperbola and replaceΒ a sec\large \ThetaΒ andΒ b tan\large \ThetaΒ in place of x and y respectively.
You will get slope of tangent to the hyperbola at point P
as (b cosec\large \Theta/ a).
Then equation of the tangent is y – b tan\large \ThetaΒ =Β (b cosec\large \Theta/ a)(x – a sec\large \Theta).
Put x = 0 in the above equation to get cooordinates of T(which is on x-axis).
TΒ \equivΒ (a cos\large \Theta, 0)
Now, N(a sec\large \Theta, 0), T(a cos\large \Theta, 0), O(0,0),
by distance formula,
OT =Β \sqrt{(a cos\large \Theta – 0)2 – (0 – 0)2}Β  = a cos\large \ThetaΒ  Β  Β  Β  Β  Β   …. (1)
andΒ ON =Β \sqrt{(a sec\large \Theta – 0)2 – (0 – 0)2}Β  = a sec\large \ThetaΒ  Β  Β  …. (2)Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β 
From (1) & (2),
OT . ONΒ  =Β  a cos\large \ThetaΒ .Β a sec\large \ThetaΒ Β 
\thereforeΒ Β Β OT . ONΒ  =Β  a2
Pls approve.

Think You Can Provide A Better Answer ?

Other Related Questions on Analytical Geometry

View all Questions Β»

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More