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

# If a tangent to the parabola y2=8x meets the x-axis at T and intersect the tangent at vertex A at P, and the rectangle TAPQ is completed, then the locus of the point Q is

A
y2+2x=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
x2+2y=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x22y=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
y22x=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A y2+2x=0 y2=8x ⇒a=2 Vertex A is (0,0). The tangent at any point (at2,2at) of the parabola y2=4ax is given by ty=x+at2. Therefore, the tangent at any point of y2=8x is ty=x+2t2. Since, the tangent at vertex A is y-axis, so, T and P are (−2t2,0) and (0,2t), respectively. Let point Q be (h,k). Then h=AT=−2t2 ⋯(1) and k=AP=2t ⋯(2) Eliminating t, using (1) and (2), we get 2h=−(k)2 ⇒k2+2h=0 Hence, the locus of Q is y2+2x=0

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Line and a Parabola
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program