Question

If p and p’ denote the lengths of the perpendicular from a focus and the centre of an ellipse with semi-major axis of length a, respectively, on a tangent to the ellipse and r denotes the focal distance of the point, then     

Solution

Correct option is

 

Let the ellipse be  and, let 

         

  

       p = Length of the perpendicular from S(ae, 0) on (i) 

  

       p' = Length of the perpendicular from O(0, 0) on (i) 

  

  

.

SIMILAR QUESTIONS

Q1

The tangent at a point  meets the auxiliany circle in two points. The chord joining them subtends a right angle at the centre. Then, the eccentricity of the ellipse is given by  

Q2

If F1 and F2 be the feet of the perpendicular from the foci S1and S2 of an ellipse  on the tangent at any point P on the ellipse, then (S1F1)(S2F2) is equal to   

Q3

The area of the rectangle formed by the perpendiculars from the centre of the ellipse to the tangent and normal at the point-whose eccentric angle is , is  

Q4

The slope of a common tangent to the ellipse  and aconcentric circle of radius r is

Q5

P is a variable point on the ellipse  with AA’ as the major axis. Then, the maximum value of the area of the triangleAPA’ is   

Q6

The equation of the ellipse whose distance between the foci is equal to 8 and distance between the directrices is 18, is

Q7

The line x = at2 meets the ellipse  in the real points iff

Q8

On the ellipse 4x2 + 9y2 = 1, the points at which the tangents are parallel to the line 8x = 9y are

Q9

Tangent is drawn to the ellipse  , then the value of θ such that sum of intercepts on axes made by the tangent is minimum is  

Q10

If circumcentre of an equilateral triangle inscribed in  with vertices having eccentric angle α, β, γ respectively is (x1y1) then