Flag Discuss with Askiitians Tutors> he angle between the tangents to the para...
question mark

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

moidin afsan , 10 Years ago
Grade 11
anser 1 Answers
Jitender Singh

Last Activity: 10 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

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free