JEE Advance - Mathematics (1996 - No. 10)
The angle between a pair of tangents drawn from a point P to the circle $${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\, + \,9\,{\sin ^2}\,\alpha \, + \,13\,{\cos ^2}\,\alpha \, = \,0$$ is $$2\,\alpha $$.
The equation of the locus of the point P is
The equation of the locus of the point P is
$${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\, + \,4\, = \,0$$
$${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\,\, - \,9\,\, = \,0$$
$${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\,\, - \,4\,\, = \,0$$
$${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\,\, + \,9\,\, = \,0$$