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

AB, AC are tangents to a parabola y2=4ax If l1,l2.l3 are the lengths of perpendiculars from A, B, C on any tangent to the parabola, then

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

The correct option is B are in G.P
Let B(at21,2at1)C(at22,2at2)
Since AB, AC are tangents to the parabola we have A[at1t2,a(t1+t2)]
Eqution of a tangent to y2=4ax is mx+am........(1)
l2 =Length of the lr from B to (1) = mat212at1+am1+m2
Similarly l3 =mat222at2+am1+m2
l2=Length of the lr from A to the line (1)=mat1t2a(t1+t2)+am1+m2
l2l3=[mat212at1+am1+m2][mat222at2+am1+m2]
m2a2t21t22+a2(t22+2t1t2+t22)+a2m22a2mt1(t1+t2)2a2m(t1+t2)+2a2t1t21+m2
=[mat1t2a(t1+t2)+am1+m2]=t21
l2,l1,l3 are in G.P.

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon