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

If the straight line xcosα+ysinα=p touches the curve x2a2y2b2=1, then prove that a2cos2αb2sin2α=p2.

Open in App
Solution

Let the line xcosα+ysinα=p touches the curve at point P(x1,y1)

The equation of tangent at P(x1,y1)

xx1a2yy1b2=1 ...(1)

Here both the equation represent same line

Now the equation xcosα+ysinα=p

or xαcosα+ysinαp=1....(2)

Now coefficient of line (1) and (2) are same

x1a2=cosαp and y1b2=sinαp

or, x1=a2cosαp and y1=b2sinαp

These two points lies on the equation of straight line

a2cos2αpb2sin2αp=p

or, a2cos2αb2sin2α=p2 hence prove

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometrical Interpretation of a Derivative
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon