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

Normals are drawn from the point P with slopes m 1 , m 2 , m 3 to the parabola y 2 = 4x. If locus of P with m 1 m 2 = α is a part of parabola itself, then find α.

Normals are drawn from the point P with slopes m1, m2, m3 to the parabola y2 = 4x. If locus of P with m1m2 = α is a part of parabola itself, then find α.

Grade:11

1 Answers

Arun
25763 Points
3 years ago
.3is y = mx – 2am – am = 4ax.2yThe equation of the normal to the parabola 

Hence, the equation of the normal to the parabola y2 = 4x is y = mx – 2m – m3.

Now, if it passes through (h, k), then we have k =  mh – 2m – m3

This can be written as m+ m(2-h) + k = 0 …. (1)

Here, m1 + m2 + m3 = 0

m1m2 + m2m+ m3m1 = 2 - h

Also, m1m2m3 = -k, where m1m= α

Now, this gives m= -k/α and this must satisfy equation (1).

Hence, we have (-k/α)3 + (-k/α)(2-h) + k = 0

Solving this, we get k2 = α2h – 2α2 + α3

And so we have y2 = α2x – 2α2 + α3

On comparing this equation with y2 = 4x we get

α= 4 and -2α+ α3 = 0

This gives α = 2.

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