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

Show that the locus of a point that divides a chord of slope 2 of y2=4x internally in the ratio 1:2 is a parabola. Also find its vertex.

A
(49,89)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(29,49)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(29,89)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
(49,49)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C (29,89)
Let the two points on the given parabola be (t12, 2t1) and (t22, 2t2). Slope of the line joining these points is
2=[2t2-2t1]/[t22-t12]=2/t1+t2

=> t1 + t2 = 1
Hence the two points become (t12 , 2t1) and ((1 − t1)2 , 2(1 − t1))
Let (h , k) be the point which divides these points in the ratio 1 : 2
h=(1-t1)2+2t1/3=1-2t1+3t12/3 ....(1)

k=[2(1-t1)+4t1]/3=2+2t1/3 ....(2)
Eliminating t1 from (1) and (2), we find that 4h = 9k2 − 16k + 8
Hence locus of (h , k) is
(y-8/9)2=4/9(x-2/9)
This is a parabola with vertex (2/9 , 8/9)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Chords and Pair of Tangents
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon