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



Analytical Geometry

Neeraj Agarwal's Avatar
Blazing goIITian

Joined: 22 Jan 2007
Post: 2039
24 Feb 2007 15:10:10 IST
0 People liked this
7
643 View Post
parabola
None

The tangent and normal at the point P(at2,2at) to the parabola y2=4ax meet the x-axis in T and G respectively,then angle at which the tangent at P to the parabola is inclined to the tangent at P to the circle through P,T,G is?

[ans:tan-1(t)]
I'm getting different ans


Share this article on:

Comments (7)


New kid on the Block

Joined: 24 Feb 2007
Posts: 3
24 Feb 2007 15:17:12 IST
0 people liked this

ghj

New kid on the Block

Joined: 17 Feb 2007
Posts: 28
24 Feb 2007 18:09:57 IST
0 people liked this

 according to your question a tangent  cuts x-axis in 2 different points
is at possible??

Blazing goIITian

Joined: 9 Feb 2007
Posts: 471
24 Feb 2007 18:16:47 IST
0 people liked this


neeraj i suppose,
u can find the equation of the circle by the given three points and then find the tangent due to P on the circle and then find the angle b/w them by the formula of tanQ!
Neeraj Agarwal's Avatar

Blazing goIITian

Joined: 22 Jan 2007
Posts: 2039
24 Feb 2007 21:09:06 IST
0 people liked this

avdesh...I tried it but am getting different ans..

Blazing goIITian

Joined: 9 Feb 2007
Posts: 471
24 Feb 2007 21:26:28 IST
0 people liked this

then ur answer is correct...anyways i think this is lengthy but sure method
snehi's Avatar

Cool goIITian

Joined: 23 Feb 2007
Posts: 52
24 Feb 2007 22:11:41 IST
1 people liked this

Hi neeraj,
The circle is nothing but the 1 with diameter as TG and center at S(a,0) ;
Let the PTS =  ;{ where Tan  = 1 / t }
Let the angle bt tangents be  ;
So, ext angle PSG = { +( /2 - )}
Just expand..TanPSG  { = 2t / (t2-1) } ;
Solve for cot  ;{u get it as 1/t }
So,   = Tan-1(1/t) ....ans.
Bipin Dubey's Avatar

Forum Expert
Joined: 23 Jan 2007
Posts: 7942
25 Feb 2007 14:48:44 IST
0 people liked this

You just draw the figure.Since tangent and normal at P are perpendicular to each other,so TPG = 900.
This is the angle contained in a semicircle and hence TG would be the diameter of the circle passing through P,T and G.

In equation of tangent and normal put y=0 to get T and G.
Then T is (-at2,0)  and  G is  (2a - at2,0)
Hence centre of the circle is (a,0) which is the focus of parabola.

Slope of normal to the circle at P = 2at/(at2-a) = 2t/(t2-1)
Hence slope of tangent to the circle at P = -1/(slope of normal) = (1-t2)/2t

Also slope of tangent at P to parabola = 1/t

Now slopes of two lines are known and you can easily find the angle between them.

Best Wishes



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

Name

Mobile No.

Find Posts by Topics

Physics.

Topics

Mathematics.

Chemistry.

Biology

Parents

Board

Fun Zone

Sponsored Ads