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

If from a point A, the two tangents drawn to the parabola y2=4ax are normals to the parabola x2=4by, then

A
a2>2b2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
a2<4b2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
a2>8b2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
a=2b
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B a2>8b2
For y2=4ax, the equation of a tangent can be written as :
y=mx+am
For x2=4by, the equation of a normal can be written as :
y=mx+2b+bm2
Comparing the coefficients we get,
am=+2b+bm2
On simplifying we get,
2bm2am+b=0
The roots of this equation must be real and distinct. Hence,
Δ>0
a28b2>0
a2>8b2
Hence,
Option C is correct.

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