CIRCLE 3

The angle between a pair of tangents drawn from a point P to the circle $x^2+y^2+4x-6y+9\ \sin^2\alpha+13\cos^2\alpha=0\ is\ 2\alpha.$ The equation of the locus of the point P is 

•  $x^2+y^2+4x-6y+4=0$  

•  $x^2+y^2+4x-6y-9=0$  

•  $x^2+y^2+4x-6y-4=0$  

•  $x^2+y^2+4x-6y+9=0$  

Let L be a straight line through the origin and $L_2$  be the straight line x + y = 1. If the intercepts made by the circle  $x^2+y^2-x+3y=0\ on\ L_1\ and\ L_2$  and equal, then which of the following equations can represent  $L_1?$  

• x + y = 0

• x - y = 0

• x + 7y = 0

• x - 7y = 0

The radius of the circle, having centre at (2,1), whose one of the chord is a diameter of the circle $x^2+y^2-2x-6y+6=0$  

• 1

• 2

• 3

•  $\sqrt{3}$  

IF (-3, 2) lies on the circle  $x^2+y^2+2gx+2fy+c=0,$  which is concentric with the circle  $x^2+y^2+6x+8y-5=0,$   the c is.

• 11

• - 11

• 24

• none of these

The circle $x^2+y^2-6x-10y+c=0$  does not intersect or touch either axis and the point (1, 4) is inside the circle. Then the range of possible values of c is given by:

• c > 9

• c > 25

• c > 29

• 25 < c < 29

The length of the tangent drawn from any point on the circle $x^2+^2y^2+2gx\ +\ 2fy\ +\ p=0$  to the circle  $x^2+y^2+2gx\ +\ 2fy\ +\ q\ =0\ is\ :$  

•  $\sqrt{q-p}$  

•  $\sqrt{p-q}$  

•  $\sqrt{q+p}$  

• none

The angle between the two tangents from the origin to the circle $x-7^2+\left(y+1\right)^2=25\ equals$  

•  $\frac{\pi}{4}$  

•  $\frac{\pi}{3}$  

•  $\frac{\pi}{2}$  

• none

The circumference of the circle $x^2+y^2-2x+8y-q=0\$  is bisected by the circle  $x^2+y^2+4x+12y+p=0,$  then p + q  is equal to :

• 25

• 100

• 10

• 48

Two this rods AB and CD of lengths 2a and 2b move along OX and OY respectively, when 'Q' is the origin. The equation of the locus of the centre of the circle passing through the extremities of the two rods is:

• $x^2+y^2=a^2+b^2$

• $x^2-y^2=a^2-b^2$

• $x^2+y^2=a^2-b^2$

• $x^2-y^2=a^2+b^2$

Let x and y be the real numbers satisfying the equation $x^2-4x+y^2+3=0.$  If the maximum and minimum values of  $x^2+y^2\ are\ M\ and\ m\ respectively,\$  then the numerical value of M -- m is :

• 2

• 8

• 15

• none of these