Question

Find the condition on a and b for which two distinct chords of the ellipse  passing through (a, –b) are bisected by the line x + y = b

Solution

Correct option is

 

Let (tb – t) be a point on the line x + y = b

Then equation of chord whose mid point (tb – t) is     

     

(a, –b) lies on (i) then  

     

     

Since t is real   

      

    

, which is the required condition.

SIMILAR QUESTIONS

Q1

Find the lengths and equations of the focal radii drawn from the point  on the ellipse 25x2 + 16y2 = 1600.

Q2

 

For what value of λ dose the line y = x + λ touches the ellipse

9x2 + 16y2 = 144.

Q3

Find the equations of the tangents to the ellipse  which are perpendicular to the line y + 2x = 4.

Q4

Find the locus of the foot of the perpendicular drawn from centre upon any tangent to the ellipse .

Q5

Find the locus of the points of the intersection of tangents to ellipse  which make an angle θ.

Q6

Find the locus of the poles of tangents to  with respect to the concentric ellipse .  

Q7

 

Determine the equation of major and minor axes of the ellipse  

       

Also, find its centre, length of the latusrectum and eccentricity.

Q8

 

Find the locus of the centroid of an equilateral triangle inscribed in the ellipse     

                  

Q9

If SY and S1Y1 be perpendiculars from the foci upon the tangent atP of an ellipse, then Y and Y1 lie on the auxiliary circle andSY.S1Y1 =    

Q10

Let P be a point on the ellipse , 0 < b < a. Let the line parallel to y-axis passes through P meet the circle  at the point Q, such that P and Q are the same side of x-axis. For two positive  real numbers r and s, find the locus of the point Ron PQ such that PR : RQ = r : s as P varies over the ellipse.