The distance between the chords of contact of tangents to the circle `x^2+y^2+2gx +2fy+c=0` from the origin & the point (g,f) is

The equation of the tangent to circle x^(2)+y^(2)+2g x+2fy=0 at origin is :

Let the midpoint of the chord of contact of tangents drawn from A to the circle x^(2) + y^(2) = 4 be M(1, -1) and the points of contact be B and C

The distance between the origin and the tangent to the curve y=e^(2x)+x^2 drawn at the point x=0 is

Length of the tangent. Prove that the length t o f the tangent from the point P (x_(1), y(1)) to the circle x^(2) div y^(2) div 2gx div 2fy div c = 0 is given by t=sqrt(x_(1)^(2)+y_(1)^(2)+2gx_(1)+2fy_(1)+c) Hence, find the length of the tangent (i) to the circle x^(2) + y^(2) -2x-3y-1 = 0 from the origin, (2,5) (ii) to the circle x^(2)+y^(2)-6x+18y+4=-0 from the origin (iii) to the circle 3x^(2) + 3y^(2)- 7x - 6y = 12 from the point (6, -7) (iv) to the circle x^(2) + y^(2) - 4 y - 5 = 0 from the point (4, 5).

The chord of contact of tangents from 3 points A, B, C to the circle x^(2) + y^(2) =4 are concurrent, then the points A, B and C are:

The point of contact of a tangent from the point (1, 2) to the circle x^2 + y^2 = 1 has the coordinates :

If x=3 is the chord of the contact of the circle x^2 + y^2 = 81, then the equation of the corresponding pair of tangents, is

If O is the origin and OP, OQ are distinct tangents to the circle x^(2)+y^(2)+2gx+2fy+c=0 then the circumcentre of the triangle OPQ is

Find the area of equilateral triangle inscribed in a circle x^2+y^2+2gx+2fy+c=0

The circle x^(2) + y^(2) + 2g x + 2fy + c = 0 does not intersect the y-axis if