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

Find the locus of point of intersection of tangents to the parabola y2=4ax which include an angle of 45.

A
(x+2a)2=y24ax
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(x+a)2=y24ax
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(x+a)2=y2+4ax
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(x+a)2=y24ax
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is B (x+a)2=y24ax
Let the tangents be drawn at the points t1 and t2
and (h,k) be their point of intersection.
h=at1t2,k=a(t1+t2) ...(1)Also their equations aret1y=x+at21,t2y=x+at22
Also their slope are
1/t1 and 1/t2 ...(2)
If they include an angle α, then
tanα=(t2t1)t1t2+1
or tan2α(1+t1t2)2={(t1+t2)24t1t2}
or tan2α(1+ha)2={k2a24ha}
or tan2α(h+a)2=(k24ah)
Hence the required locus is
(x+a)2tan2α=y24ax.
In case the tangents include an angle of 45 then
tan45=1, we get the locus as
(x+a)2=y24ax

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