Question

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

Solution

Correct option is

Suppose (h, k) is mid-point of focal chord.

Then its equation is T = S1

  

Since it passes through focus (ae, 0)

  

  Locus of (h, k) is

      .

SIMILAR QUESTIONS

Q1

Tangents are drawn to the ellipse  at the end of latus rectum. Find the area of quadrilateral so formed   

Q2

The eccentricity of the ellipse which meets the straight line  on the axis of x and the straight line  on the axis of y and whose axes lies along the axes of coordinates is

Q3

The line lx + my + n = 0 is a normal to the ellipse  if

Q4

If the normal at any point P on the ellipse cuts the major and minor axes in G and g respectively and C be the center of the ellipse

Q5

The angle between the pair of tangents drawn from the point (1, 2) to the ellipse 3x2 + 2y2 = 5 is

Q6

The ellipse  cuts x-axis at A and A’ and y-axis at Band B’. The line joining the focus S and B makes an angle  with x-axis. The eccentricity of the ellipse is

Q7

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

Q8

The equation  represents an ellipse, if

Q9

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 

Q10

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