Question

The tangent and normal to the ellipse x2 + 4y2 = 4 at a point P(θ) in second quadrant, meet the major axis in Q and R respectively. If QR = 2, then cos θ is equal to

Solution

Correct option is

    

Equation of the tangent at                … (1)

   

equation of the normal at

Therefore   

 

   

  

 as the point is in quadrant second .

SIMILAR QUESTIONS

Q1

The equation of the ellipse whose centre is (2, –3), one of the foci is (3, –3) and the responding vertex is (4, –3) is

Q2

Find the eccentricity of the ellipse, whose foci are (–3, 4) and (3, –4) and which passes through the point (1, 2)

Q3

If  is a tangent to the ellipse , then find out the eccentric angle of the point of tangency.

Q4

For what value of λ dose the line y = x + λ touches the ellipse 9x2 + 16y2 = 144.

Q5

Find the equations of the tangents to the ellipse 3x2 + 4y2 = 12 which perpendicular to the line y + 2x = 4.

Q6

Find the equation of pair of tangents drawn from the point (1, 2) and (2, 1) to the ellipse .

Q7

A tangent to the circle x2 + y= 5 at the point (–2, 1) intersect the ellipse  at the point A, B. If tangents to the ellipse at the point A and B intersect at point C. Find the coordinate of points C.

Q8

If the line 3y = 3x + 1 is a normal to the ellipse , then find out the length of the minor axis of the ellipse.

Q9

If SK be the perpendicular from the focus S on the tangent at any point P on the ellipse , then locus of K is 

Q10

If latus rectum of the ellipse  is equal to