The line 4x + 5y = 40 touches the ellipse + = 1 then its …

Maths Conic Sections General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

The line 4x + 5y = 40 touches the ellipse + = 1 then its point of contact is.

(5, –4)

(–5, 4))

(5, 4))

(–5, –4))

Text Solution

Verified by Experts

The correct answer is:

For line y = – x + 8 to be tangent of = 1, c 2 = a 2 m 2 + b 2 is must

Here c 2 = 64, a 2 m 2 + b 2 = 50 × + 32 = 64 ⇒ c 2 = a 2 m 2 + b 2

∴ given line is tangent to the given ellipse

Let (h, k) is point of contact then equation of tangent is

...... (i)

4x + 5y – 40 = 0 ...... (ii)

(i) and (ii) both represents same straight line, hence comparing

⇒ ∴ h = 5 , k = 4

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