Home » Ask & Discuss » Mathematics. » Analytical Geometry « Back to Discussion

Analytical Geometry

New kid on the Block

Joined:	22 Sep 2011
Post:	9

21 Jan 2012 00:31:36 IST

0 People liked this

230

Parabola.rrove

Mathematics

1) Prove that the locus of the mid point of the normal chords of the parabola y²=4ax is y²/2a +4a³/y²=x-2a.

2) for what values of a will the tangents drawn to the parabola y²=4ax from a piont not on the y-axis will be normal to the parabola x²=4ay.

3) three normals to y²=4x pass through the points (15,12). show that one of the normals is given by y=x-3. also find the equation of others.

Share this article on:

Comments (1)

Manasi

Forum Expert

Joined: 1 Dec 2006

Posts: 2108

2 Feb 2012 13:00:01 IST

Like 0 people liked this

solution to Q3:

The equation of the normal in terms of 'm' (slope) is given by,

y = mx – 2am – am³

here the parabola is y² = 4x ....i.e. a=1

therefore, the equation of the normal is y = mx – 2m – m³

now, all the 3 normals passes thru point (15,12) ...hence this point shud satisfy above equation.

substituting the value, we have 12=15m – 2m – m³

solving the equation for m, we have m = 1, 3, -4

thus the three normals are, y= x -3

y= 3x-33

y=-4x+72

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

Free Sign Up!

Preparing for IIT-JEE ?

Arihant Revision Package for IIT JEE - Books, Practice Tests + Rank Predictor

@ INR 1,995/-

For Quick Info

Find Posts by Topics

Physics.

Topics

9391

20087

3671

2186

7614

2826

2636

Mathematics.

Chemistry.

Biology

Institutes

Parents

Board

Fun Zone