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Analytical Geometry

Cool goIITian

 Joined: 23 Jun 2011 Post: 65
30 May 2012 01:02:32 IST
3 People liked this
4
295
Circles
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Analytical Geometry

Show that the line (x-2) cos theta+ (y-2)sin theta=1 touches a circle for all values of theta. Find the circle.

Hot goIITian

Joined: 13 Nov 2011
Posts: 157
30 May 2012 23:07:03 IST
3 people liked this

Since this family of lines touch a circle for all values of theta, put theta = 0 , pi/2 , -pi/2 , pi .

In the above 4 cases , you will get  x=2, y=2 , y=1 , x=1 respectively.

Since the above 4 lines are tangents to the required circle, we can say that

the circle has centre at (3/2,3/2) and has radius 1/2.

So the equation of thwe circle is

Cool goIITian

Joined: 23 Jun 2011
Posts: 65
31 May 2012 11:30:31 IST
0 people liked this

Thanks for telling me the method. But i thnk u made a mistake in the calculations. wen theta is put as 0 or pi/2, dont v gt x=3, and y =3 respectively?

Hot goIITian

Joined: 13 Nov 2011
Posts: 157
1 Jun 2012 19:15:02 IST
0 people liked this

o yes i'm sorry for the mistake

Hot goIITian

Joined: 13 Nov 2011
Posts: 157
1 Jun 2012 19:16:10 IST
0 people liked this

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