Question

The locus of the poles of normal chords of an ellipse is given by

Solution

Correct option is

                       … (1)

Equation of normal is

         

Let the pole of (2) w.r.t. (1) be (x1y1)

                    … (2)

Compare (2) and (3), we get

           

               

             

.

SIMILAR QUESTIONS

Q1

Let be the perpendicular distance from the center of the ellipse  to the tangent drawn at point P on the ellipse. If F1and F2 are the two foci of the ellipse, then. Where k =

Q2

An ellipse has eccentricity  and one focus at the point . Its one directrix is the common tangent nearer to the point P, to the circle x2 + y2 = 1 and the hyperbola x2 – y2 =1. The equation of the ellipse in the standard from is

Q3

The maximum area of an isosceles triangle inscribed in the ellipse  with its vertex at one end of the major axis is

Q4

The eccentricity of the curve x2 + 2y2 – 2x + 3+ 2 = 0 is

Q5

A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. Then angle between the tangents at P and Q of the ellipse  x2 + 2y2 = 6 is

Q6

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

Q7

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

Q8

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

Q9

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