If the circle `x^2 + y^2 + 2gx + 2fy +|sin theta| -1 = 0` passes through all the four quadrants `(|sin theta| lt 1)`. then

Radius of the circle x^(2)+y^(2)+2x cos theta+2y sin theta-8=0, is

prove that all lines represented by the equation : (2 cos theta + 3 sin theta) x + (3 cos theta - 5 sin theta) y- (5 cos theta - 2 sin theta) = 0 pass through a fixed point for all values of theta . Find the coordinates of that point.

If 3 sin 2 theta = 2 sin 3 theta and 0 lt theta lt pi , then sin theta =

If 3 sin 2 theta = 2 sin 3 theta and 0 lt theta lt pi , then sin theta =

If sin theta = k , 0 lt k lt 1 and ' theta ' does not lie in the first quadrant , then tan theta =

A variable chord of circle x^(2)+y^(2)+2gx+2fy+c=0 passes through the point P(x_(1),y_(1)) . Find the locus of the midpoint of the chord.

A variable chord of circle x^(2)+y^(2)+2gx+2fy+c=0 passes through the point P(x_(1),y_(1)) . Find the locus of the midpoint of the chord.

A variable chord of circle x^(2)+y^(2)+2gx+2fy+c=0 passes through the point P(x_(1),y_(1)) . Find the locus of the midpoint of the chord.

If 0 lt theta lt pi/2 and sin 2 theta = cos 3 theta, then the value of sin theta is-

The equation of the circle passing through the point (-1+3 cos theta, 2+3 sin theta) is