CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

If two tangents drawn from the point P to the parabola y2=12x be such that the slope of the tangent is double the other, then P lies on the curve

A
2y2=9x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
y2=9x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2y2=27x
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
y2=15x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 2y2=27x
Given a parabola ,y2=12x
There is a point P outside the parabola with coordinates(h,k).Now the equation of a tangent to the parabola y2=4ax is given by
y=mx+am;m is the slope of tangent
Here a=3
y=mx+3m
is the equation of any tangent to the parabola y2=12x.This tangent passes through point (h,k) hence
m2hkm+3=0(i)
So we can see that there are two possible values of m and hence we can have two tangents drawn to the parabola y2=12x from the point (h,k).
Also the slope of one is twice that of the other.
So say m1 & m2 are the roots of the quadratic equation(i)
Then we have
m1=2m2(ii)m1+m2=kh(iii)m1.m2=3h(iv)
Now, 2m22=3h(v)3m2=khm2=k3h(vi)
Using (vi) we can reduce (v) as 2k29h2=3h
2k2=27h
Replace k with y & h with x we have
2y2=27x

flag
Suggest Corrections
thumbs-up
0
mid-banner-image
mid-banner-image
Join BYJU'S Learning Program
Select...
similar_icon
Related Videos
thumbnail
lock
Line and a Parabola
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
Select...