Question

The locus of mid-point of the portions of the tangents to the ellipse  included between the axes is the curve 

Solution

Correct option is

Equation of tangent to ellipse  is

  y = mx + c           … (1)  where

c2 = a2m2 + b2     … (2)

by (1), – mx + y = c  the tangent meets the x-axis and y-axis at    

Mid-point of AB is (x1y1

  

On multiplying          … (3)

Put (3) in (2)    is locus of (x, y).

 

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

The equation  represents an ellipse, if

Q6

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 

Q7

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

Q8

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

Q9

If the polar with respect to the parabola y2 = 4ax touches the ellipse , then the locus of its pole is  

Q10

The area of the parallelogram formed by tangents at the extremities of two conjugate diameters of the ellipse  is equal to