A set of parallel chord of the parabola y2=4ax have their midpoint on
Let P be a point on the ellipse a2x2+b2y2=1 of eccentricity e˙ If A,A′ are the vertices and S,S are the foci of the ellipse, then find the ratio area PSS′′ : area APAprime˙
Ois the origin & also the centre of two concentric circles having radii of the inner & the outer circle as
If (5, 12) and (24, 7) are the foci of an ellipse passing through the origin, then find the eccentricity of the ellipse.
Prove that the chord of contact of the ellipse a2x2+b2y2=1 with respect to any point on the directrix is a focal chord.
If ω is one of the angles between the normals to the ellipse a2x2+b2y2=1 at the point whose eccentric angles are θ and 2π+θ , then prove that sin2θ2cotω=1−e2e2
Find the eccentricity of an ellipse a2x2+b2y2=1 whose latus rectum is half of its major axis. (a>b)
Suppose that the foci of the ellipse 9x2+5y2=1 are (f1,0)and(f2,0) where f1>0andf2<0. Let P1andP2 be two parabolas with a common vertex at (0, 0) and with foci at (f1.0)and (2f_2 , 0), respectively. LetT1 be a tangent to P1 which passes through (2f2,0) and T2 be a tangents to P2 which passes through (f1,0) . If m1 is the slope of T1 and m2 is the slope of T2, then the value of (m121+m22) is