Question

Which of the following equations represents a degenerate ellipse?

9x^2 +4y^2 = 1

x^2 y^2
---- + ---- = 2
14 19

x^2 y^2
----- = (-) ----
10 18

All of the above are degenerate ellipses.

Answer 1

What do you think?

Answer 2

The third option

Answer 3

why?

Answer 4

I honestly just guessed

Answer 5

ok, the first one is the formula of a circle \((3x)^2+(2y)^2=1\)
That shows the last one is NOT the correct answer.

Answer 6

The third one is \(\dfrac{x^2}{10}=-\dfrac{y^2}{18}\) add \(\dfrac{y^2}{18}\) both sides, what do you get?

Answer 7

y^2 ?

Answer 8

nope
it becomes
\(\dfrac{x^2}{10}+\dfrac{y^2}{18}=0\)
The standard formula of an ellipse has the right hand side =1, NOT =0, hence the third option is NOT the correct answer.

Answer 9

So it would be the first option right ?

Answer 10

the second one.

Answer 11

I was right it was the third option