If C is the center of the ellipse 9x2+16y2=144 and S is a focus, then find the ratio of CS to the semi-major axis.
If from any point P on the circle x2+y2+2gx+2fy+c=0, tangents are drawn to the circle x2+y2+2gx+2fy+csin2α+(g2+f2)cos2α=0 , then find the angle between the tangents.
Perpendiculars are drawn, respectively, from the points PandQ to the chords of contact of the points QandP with respect to a circle. Prove that the ratio of the lengths of perpendiculars is equal to the ratio of the distances of the points PandQ from the center of the circles.
The common chord of the circle x2+y2+6x+8y−7=0 and a circle passing through the origin and touching the line y=x always passes through the point. (−21,21) (b) (1, 1) (21,21) (d) none of these
Two circle are externally tangent. Lines PAB and PA′B′ are common tangents with AandA′ on the smaller circle and BprimeandB′ the on the larger circle. If PA=AB=4, then the square of the radius of the circle is___________
Tangents are drawn to the circle x2+y2=a2 from two points on the axis of x, equidistant from the point (k,0)˙ Show that the locus of their intersection is ky2=a2(k−x)˙