Question

The tangent and the normal to the ellipse x2 + 4y2 = 4 at a point P on it meet the major axis in Q and R respectively. If QR = 2, then the eccentric angle of P is

Solution

Correct option is

x2 + y2 = 4           a2 = 4,  b2 = 1

Let θ be eccentric angle at any point P of ellipse,

  

Tangent at       

Normal at       

Putting values of a and b; tangent is

                         … (1)

and normal as           … (2)

Major axis is y = 0                                … (3)

(1) and (2) meet major at Q and R

            

given

Solve to get

    .

SIMILAR QUESTIONS

Q1

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

Q2

The equation  represents an ellipse, if

Q3

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 

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

If CP and CD is a pair of semi-conjugate diameters of the ellipse,

, then CP2 + CD2 =