0

Guest

Courses New

he angle between the tangents to the parabola y^2=4ax at the points whrer ti intersects the line x-y=a

he angle between the tangents to the parabola y^2=4ax at the points whrer ti intersects the line x-y=a

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans: 90
Sol:
Let P(t1, 2at1) & Q(t2, 2at2) be the points on the parabola where line intersects the parabola. Then slope of tangents at P & Q would be:
\frac{1}{t_{1}}, \frac{1}{t_{2}}
Angle between tangents:
\frac{|t_{2}-t_{1}|}{1+t_{1}t_{2}}
Since both points lie on the line, we have
t_{1}^{2}-2t_{1}-1=0
t_{2}^{2}-2t_{2}-1=0
t1, t2are the roots of the equation
t^{2}-2t-1=0
Product of the roots is -1,
t_{1}t_{2}=-1
Angle is 90.
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

Think You Can Provide A Better Answer ?

Other Related Questions on Discuss with Askiitians Tutors

View all Questions »

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