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

# The normal chord of a parabola y2=4ax at a point whose ordinate is equal to abscissa, subtends a right angle at

A
focus
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
vertex
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
ends of the latusrectum
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
any point on directrix
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A focusLet P(at2,2at) be a point on the parabola y2=4ax. Then, at2=2at⇒t=2 So the coordinates of P are (4a,4a). Let PQ be a normal chord normal at P to the parabola. y+2x=12a Let the coordinates of Q be (at21,2at1). 2at1+2at21=12a⇒t21+t1−6=0⇒t1=−3 [∵t1≠2] So, the coordinates of Q are (9a,−6a). Now, slope of SP× slope of SQ =4a3a×−6a8a=−1 Thus, the normal chord makes a right angle at the focus.

Suggest Corrections
3
Join BYJU'S Learning Program
Join BYJU'S Learning Program