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Question: The equation \(\frac{x^{2}}{10 - a} + \frac{y^{2}}{4 - a}\)= 1 represents an ellipse if –...

The equation x210−a+y24−a\frac{x^{2}}{10 - a} + \frac{y^{2}}{4 - a}= 1 represents an ellipse if –

A

a< 4

B

a > 4

C

4 < a < 10

D

a > 10

Answer

a< 4

Explanation

Solution

We have x210−a\frac{x^{2}}{10 - a}+ y24−a\frac{y^{2}}{4 - a} = 1 … (1)

(1) represent an ellipse 10 – a > 0 and 4 – a > 0

\ 10 > a & a < 4

Ž a < 10 & a < 4, then a < 4.