CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find the point of contact of tangents to the parabola y2=16x which are parallel and perpendicular to the line 2x−y+5=0.

A
(16,16)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
(16,16)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(0,16)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(0,16)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A (16,16)
We know that y=mx+am is a tangent to the parabola y2=4ax
And the point of contact is (am2,2am).
Here y2=16x is the parabola
4a=16 or a=4.
Slope of the line 2xy+5=0 is 2.
Any tangent parallel to it will have its slope 2 and ar to it will have slope 12.
Hence, putting a=4,m=2 and 12 the tangents are
2xy+2=0 at (1,4) and x+2y+16=0 at (16,16)
Ans: B

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Characteristics of Sound Waves
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon