An ellipse with major axis 4 and minor axis 2 touches both …

Maths Conic Sections General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

An ellipse with major axis 4 and minor axis 2 touches both the coordinate axes, then locus of its focus is

(x 2 – y 2 ) (1 + x 2 y 2 ) = 16 x 2 y 2

(x 2 – y 2 ) (1 – x 2 y 2 ) = 16 x 2 y 2 .

(x 2 + y 2 ) (1 + x 2 y 2 ) = 16 x 2 y 2

(x 2 + y 2 ) (1 – x 2 y 2 ) = 16 x 2 y 2 .

Text Solution

Verified by Experts

The correct answer is:

Statement-1 : Let focus of ellipse are ( α , β ) and (h, k)

 Product of length of perpendicular dropped from focus on any tangent is b 2

∴ h α = 1 ⇒ α =

k β = 1 ⇒ β =

Now distance between focii is 2 ae

∴ (h – α ) 2 + (k + β ) 2 = = 12

+ = 12

After simplification (h 2 + k 2 ) (1 + h 2 k 2 ) = 16h 2 k 2

Hence the locus (x 2 + y 2 ) (1 + x 2 y 2 ) = 16x 2 y 2

Statement-2 Standard result.

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