Tangents `PT_1, and PT_2`, are drawn from a point P to the circle `x^2 +y^2=a^2`. If the point P lies on the line `Px +qy + r = 0`, then the locus of the centre of circumcircle of the triangle `PT_1T_2` is

A pair of tangents are drawn from a point P to the circle x^2+y^2=1 . If the tangents make an intercept of 2 on the line x=1 then the locus of P is

If the tangent from a point p to the circle x^2+y^2=1 is perpendicular to the tangent from p to the circle x^2 +y^2 = 3 , then the locus of p is

Tangents PA and PB are drawn to the circle x^2+y^2=4 ,then locus of the point P if PAB is an equilateral triangle ,is equal to

Tangents PA and PB are drawn to the circle x^2 +y^2=8 from any arbitrary point P on the line x+y =4 . The locus of mid-point of chord of contact AB is

Tangents drawn from the point P(1,8) to the circle x^2 +y^2 -6x -4y-11=0 touch the circle at the points A&B ifR is the radius of circum circle of triangle PAB then [R]-

P is a variable point of the line L = 0. Tangents are drawn to the circle x^2 + y^2 = 4 from P to touch it at Q and R. The parallelogram PQSR is completed. If L = 2x + y - 6 = 0 , then the locus of circumcetre of trianglePQR is -

Tangents are drawn to a unit circle with centre at the origin from each point on the line 2x + y = 4 . Then the equation to the locus of the middle point of the chord of contact is

The tangents PA and PB are drawn from any point P of the circle x^(2)+y^(2)=2a^(2) to the circle x^(2)+y^(2)=a^(2) . The chord of contact AB on extending meets again the first circle at the points A' and B'. The locus of the point of intersection of tangents at A' and B' may be given as

If a tangent to the circle x^(2)+y^(2)=1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is :

If tangents P Qa n dP R are drawn from a variable point P to thehyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(a > b), so that the fourth vertex S of parallelogram P Q S R lies on the circumcircle of triangle P Q R , then the locus of P is x^2+y^2=b^2 (b) x^2+y^2=a^2 x^2+y^2=a^2-b^2 (d) none of these