Question

The locus of the foot of the perpendiculars to any tangent of an ellipse from the foci is

Solution

Correct option is

Auxiliary circle

Tangent to ellipse is

                                  … (1)

Slope of this line is m

This passes through (ae, 0). So equation is

             my + x – ae = 0                                   … (2)

The locus of foot of ⊥ is obtained by eliminating m between (1) and (2)

             x2 + y2 = a2 is locus  circle.

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

If the angle between the straight lines joining foci and the ends of minor axis of the ellipse  is 900 then the eccentricity is

Q7

The tangent and the normal to the ellipse x2 + 4y2 = 4 at a point P on it meet the major axis in Q and R respectively. If QR = 2, then the eccentric angle of P is

Q8

If CP and CD is a pair of semi-conjugate diameters of the ellipse,

, then CP2 + CD2 =

Q9

The line y = 2t2 meets the ellipse  in real point if

Q10

The product of the perpendiculars from the foci upon any tangent to the ellipse  is