The two circles x2+y2=axand x2+y2=c2(c>0)touch each other if :
If the normal at any point P on the ellipse a2x2+b2y2=1 meets the axes at Gandg respectively, then find the raio PG:Pg= (a) a:b (b) a2:b2 (c) b:a (d) b2:a2
A tangent having slope of −34 to the ellipse 18x2+32y2=1 intersects the major and minor axes at points AandB, respectively. If C is the center of the ellipse, then find area of triangle ABC˙
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.
Prove that any point on the ellipse whose foci are (−1,0) and (7,0) and eccentricity is 21 is (3+8cosθ,43sinθ),θ∈R˙
Find the center, foci, the length of the axes, and the eccentricity of the ellipse 2x2+3y2−4x−12y+13=0
Find the equation of the ellipse (referred to its axes as the axes of xandy , respectively) whose foci are (±2,0) and eccentricity is 21
Find the coordinates of the foci and the vertices the eccentricity and the length of the latus of rectum of the hyperbola 9y2−27x2=1