Question

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  

Solution

Correct option is

 

The equation of the tangent at

 

           

The combined equation of the chords joining the points of intersection of (i) and the auxiliary circle x2 + y2 = a2 is  

      

The lines given by this equation are at right angles. 

∴ Coeff. of x2 + Coeff. of y2 = 0   

  

  

  

  

  

SIMILAR QUESTIONS

Q1

The number of values of c such that the straight line y = 4x + ctouches the curve , is  

Q2

, then PF1 + PF2 equals

Q3

An ellipse slides between two perpendicular straight lines. Then, the locus of its centre is a/an

Q4

The sum of the squares of the perpendicular on any tangent to the ellipse  from two points on the minor axis, each at a distance  from the centre is 

Q5

The eccentric angle of a point on the ellipse  whose distance from the centre of the ellipse is 2, is

Q6

If any tangent to the ellipse  intercepts equal length lon the axes, then =

Q7

The ellipse x2 + 4y2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then, the equation of the ellipse is  

Q8

A focus of an ellipse is at the origin. The directrix is the line  x = 4 and the eccentricity is 1/2. Then the length of the semi-major axis, is  

Q9

In an ellipse, the distance between its foci is 6 and minor axis is 8. The eccentricity is 

Q10

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