Question

The area of the parallelogram formed by tangents at the extremities of two conjugate diameters of the ellipse  is equal to

Solution

Correct option is

4ab

Let POP’ and QOQ’ be conjugate diameters of the ellipse. Then

             

        

Then   

Tangents are drawn at these extremites to from parallelogramEFGH.

If    Δ = area of FEGH = 4. Area of  gm OPEQ

         = 4 . 2 . Area of ΔOPQ

         

SIMILAR QUESTIONS

Q1

The angle between the pair of tangents drawn from the point (1, 2) to the ellipse 3x2 + 2y2 = 5 is

Q2

The ellipse  cuts x-axis at A and A’ and y-axis at Band B’. The line joining the focus S and B makes an angle  with x-axis. The eccentricity of the ellipse is

Q3

A circle is drawn on the major axis of the ellipse 9x2 + 16y2 = 144 as diameter. The equation of circle is

Q4

The equation  represents an ellipse, if

Q5

S and T are the foci of an ellipse and B is an end of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is 

Q6

The locus of mid-points of focal chords of the ellipse  is 

Q7

If  touches the ellipse , then its eccentricity angle θ is equal to

Q8

If the polar with respect to the parabola y2 = 4ax touches the ellipse , then the locus of its pole is  

Q9

The locus of mid-point of the portions of the tangents to the ellipse  included between the axes is the curve 

Q10

If the angle between the straight lines joining foci and the ends of minor axis of the ellipse  is 900 then the eccentricity is