Question

Let S and S’ be two foci of the ellipse . If a circle described on SS’ as diameter intersects the ellipse in real and distinct points, then the eccentricity e of the ellipse satisfies   

Solution

Correct option is

 

The equation of the circle described on SS’ as a diameter is  

      

  

The abscissa of the points of intersection of the ellipse and this circle are the roots of the equation   

       

  

  

  

This will give distinct values of x is 

SIMILAR QUESTIONS

Q1

The eccentricity of the ellipse with centre at the origin which meets the straight line  on the axis of x and the straight line  on the axis of y and whose axes lie along the axes of  coordinates is

Q2

 

The radius of the circle passing through the foci of the ellipse

9x2 + 16y2 = 144 and having its centre at (0, 3), is 

Q3

An ellipse has OB as a semi-minor axis, FF’ as its foci and the angle FBF’ is a right angle. Then, the eccentricity of the ellipse is

Q4

The focus of an ellipse is (–1, –1) and the corresponding directix is x – y + 3 = 0. If the eccentricity of the ellipse is 1/2, then the coordinates of the centre of the ellipse are 

Q5

 

The equation of the ellipse with its centre at (1, 2), one focus at (6, 2) and passing through (4, 6) is

Q6

Tangents are drawn to the ellipse  and the circle x2 + y2 = a2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then, the greatest acute angle between these tangents is given by 

Q7

The area of the quadrilateral formed by the tangents at the end-points of latusrecta to the ellipse 

Q8

If α – β = constant, then the locus of the point of intersection of tangents at  to the ellipse   

Q9

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

Q10

If PSQ is a focal chord of the ellipse , then the harmonic mean of SP and SQ is