Tangents are drawn from external poinl `P(6,8)` to the circle `x^2+y^2 =r^2` find the radius r of the circle such that area of triangle formed by the tangents and chord of contact is maximum is (A) 25 (B) 15 (C) 5 (D) none

The number of tangents that can be drawn from the point (8,6) to the circle x^2+y^2-100=0 is

Tangent are drawn from the point (3, 2) to the ellipse x^2+4y^2=9 . Find the equation to their chord of contact and the middle point of this chord of contact.

A variable chord is drawn through the origin to the circle x^2+y^2-2a x=0 . Find the locus of the center of the circle drawn on this chord as diameter.

Find the equations of the tangents drawn from the point A(3, 2) to the circle x^2 + y^2 + 4x + 6y + 8 = 0

Tangent drawn from the point (a ,3) to the circle 2x^2+2y^2=25 will be perpendicular to each other if a equals (a) 5 (b) -4 (c) 4 (d) -5

Tangent drawn from the point P(4,0) to the circle x^2+y^2=8 touches it at the point A in the first quadrant. Find the coordinates of another point B on the circle such that A B=4 .

Transverse common tangents are drawn from O to the two circles C_1,C_2 with 4, 2 respectively. Then the ratio of the areas of triangles formed by the tangents drawn from O to the circles C_1 and C_2 and chord of contacts of O w.r.t the circles C_1 and C_2 respectively is

Tangents are drawn to the circle x^2+y^2=9 at the points where it is met by the circle x^2+y^2+3x+4y+2=0 . Find the point of intersection of these tangents.

Tangents are drawn from any point on the circle x^(2)+y^(2) = 41 to the ellipse (x^(2))/(25)+(y^(2))/(16) =1 then the angle between the two tangents is

Let A B be chord of contact of the point (5,-5) w.r.t the circle x^2+y^2=5 . Then find the locus of the orthocentre of the triangle P A B , where P is any point moving on the circle.