Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The locus of the foot of the perpendicular drawn from the centre to any tangent to the ellipse x 2 /a 2 + y 2 /b 2 = 1 is -
Text Solution
Verified by ExpertsThe correct answer is:
D
Equation of any tangent to the ellipse is
y = mx + 
… (1)
Equation of the line through the centre (0, 0) perpendicular to (1) is
y = (–1/m) x … (2)
Eliminating m from (1) and (2) we get the required locus of the foot of the perpendicular
as y = – 
+ 
or (x 2 + y 2 ) 2 = a 2 x 2 + b 2 y 2 .
Which does not represent a circle, an ellipse or a hyperbola.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is
If distance between the directrices be thrice the distance between the foci, then eccentricity of e…
The equation of the ellipse whose centre is at origin and which passes through the points (–3, 1) a…
If the eccentricity of an ellipse be 5/8 and the distance between its foci be 10, then its latus re…
If the foci and vertices of an ellipse be and , then the minor axis of the ellipse is
The equations of the directrices of the ellipse are