#### Thank you for registering.

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

Click to Chat

1800-5470-145

+91 7353221155

CART 0

• 0
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 locus of a point from which 3 normals can be drawn to y2=4x such that the sum of the angles made by them with the axis is 3pie/4 is a a) parabolab) circlec) straight lined) none of these

10 years ago

Dear student,

Write the equation of normal to parabola.

Normal at the Point (x1, y1 ):

The equation of the tangent at the point (x1, y1) is yy1 = 2a(x + x1). Since the slope of
tangent = 2a/y1 , slope of normal is -y1/ 2a . Also it passes through (x1, y1).

Hence its equation is y - y1 = y1 / 2a ( x - x1 )                          . . . . .   (i)

Normal in Terms of m:

In equation (i), put - y1 / 2a = m so that y1 = -2am and x1 = y12 / 4a = am2, then the equation becomes

y = mx - 2am - am3                                                     . . . . .  (ii)

where m is a parameter. Equation (ii) is the normal at the point (am2, -2am) of the parabola.

All the best.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Sagar Singh

B.Tech, IIT Delhi

sagarsingh24.iitd@gmail.com