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

# A tangent to the parabola y2=4ax meets x axis at a point T. This tangent meets the tangent at the vertex at point P. If rectangle TAPQ is completed then the locus of Q is.

A

Circle

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B

Straight line

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C

parabola

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

Ellipse

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is C parabola Here we will make use of the parametric form for tangents. The tangent at any point B (at2,2at) to the parabola is, ty=x+at2 lets draw a figure representing given conditions Here Q is the required locus point given by (h, k) and forms the vertex of □QPAT. We can obtain points P and T by solving equation of tangents at x and y axis. T≡(−at2,0) P≡(0,at) Also A≡(0,0) Since Q≡(h,k) h=AT=−at2 - - - - - - (1) k = AP = at - - - - - - (2) eliminating t from (1) & (2) k2+ah=0 hence locus of Q is, y2+ax=0 y2=−ax which represents a parabola.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
T
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program