The Curve Represented By  

S(3, 4) and S’(9, 12) are two foci of an ellipse. If the foot of the perpendicular from S on a tangent to the ellipse has the coordinates (1, –4), then the eccentricity of the ellipse is  

The tangent at a point P(θ) to the ellipse  cuts the auxiliary circle at points Q and R. If QR subtends a right angle at the centre C of the ellipse, then the eccentricity of the ellipse is

Let d₁ and d₂ be the lengths of the perpendiculars drawn from fociS and S’ of the ellipse  to the tangent at any point P on the ellipse. Then, SP : SP’ = 

The eccentricity of an ellipse with centre at the origin and axes along the coordinate axes, is 1/2. If one of the directrices is x = 4, then the equation of the ellipse is  

If the tangents are drawn to the ellipse x² + 2y² = 2, then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

If A bar of given length moves with its extremities on two fixed straight lines at right angles, then the locus of any point on the bar describes a/an

The normal at a point P on the ellipse x² + 4y² = 16 meets the x-axis at Q. If M is the mid-point of the line segment PQ then the locus of M intersects the latusrectums of the given ellipse at the points    

The equation  represents an ellipse, if  

The curve with parametric equations 

Length of the major axis of the ellipse , is