Question

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

Solution

Correct option is

27 sq.units

 

We have, 

       

Let e be the eccentricity of this ellipse. Then, 

       

The coordinates of the end-points of latusrecta are

       

The equations of tangents at these points are   

         

    

       

    

Clearly, these tangents from a parallelogram whose area is given by 

      .

⇒   A = 27 sq.units.  

SIMILAR QUESTIONS

Q1

A tangent to the ellipse  is cut by the tangent at the extremities of the major axis at T and T’. The circle on TT’ as diameter passes through the point

Q2

 

If C is the centre and A, B are two points on the conic

4x2 + 9y2 – 8x – 36y + 4 = 0 such that ∠ACB = π/2 then CA–2 +CB–2 is equal to  

Q3

Ellipses which are drawn with the same two perpendicular lines as axes and with the sum of the reciprocals of squares of the lengths of their semi-major axis and semi-minor axis equal to a constant have only.

Q4

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

Q5

 

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

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

Q6

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

Q7

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 

Q8

 

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

Q9

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 

Q10

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