wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Tangents are drawn from a point P to the parabola y2=4ax. If the chord of contact of the parabola is a tangent to the hyperbola x2a2y2b2=1, then the locus of P is

A
a2x2=a4y2b2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
4a2x2=4a4y2b2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
4a2x2=a4y2b2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
a2x2=4a4y2b2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 4a2x2=4a4y2b2
Let the coordiates of point P be (h,k)
then the equation of the chord of contact of the parabola is
yk=2a(x+h)
y=2akx+2ahk(1)
Since equation (1) is a tangent to the hyperbola,
x2a2y2b2=1
So,
c2=a2m2b2(2ahk)2=a2(2ak)2b24a2h2=4a4k2b2

Hence the locus of P(h,k) is
4a2x2=4a4y2b2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Lines and Points
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon