Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

The tangents at the points P(ap2, 2ap) and Q(aq2, 2aq) on the parabola y2 = 4ax intersect at the point R. Given that the tangent at P is perpendicular to the chord OQ, where O is the origin, find the equation of the locus of R as p varies.

The tangents at the points P(ap2, 2ap) and Q(aq2, 2aq) on the parabola y2 = 4ax
intersect at the point R. Given that the tangent at P is perpendicular to the chord
OQ, where O is the origin, find the equation of the locus of R as p varies.
 

Grade:12

1 Answers

Aditya Gupta
2080 Points
one year ago
point of intersection of tangents can be easily found out to be R(h. k) as
h= apq and k = a(p+q)
now,  tangent at P is perpendicular to the chord OQ. so prod of slopes will be – 1.
or (1/p)*(2aq/aq^2)= – 1
pq= – 2
apq= – 2a
h= – 2a
replacing h by x
reqd locus: x+2a= 0
kindly approve :))

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free