The equation (\frac{x^{2}}{1 - r})– (\frac{y^{2}}{1 + r})= 1... | MATH - ELLIPSE | SolveeIt

The equation $\frac{x^{2}}{1 - r}$ – $\frac{y^{2}}{1 + r}$ = 1, r > 1 represents

An ellipse

A hyperbola

A circle

None of these

Answer

None of these

Explanation

$\frac{x^{2}}{1 - r}$ – $\frac{y^{2}}{1 + r}$ = 1; (r > 1)

Let r = 2 Ž $\frac{x^{2}}{( - 1)}$ – $\frac{y^{2}}{3}$ = 1

Ž 3x² + y² = –3

Ž 3x² + y² + 3 = 0

It is not a circle, ellipse and hyperbola.

\ none of these

Note : If (r < –1) Ž then equation is an ellipse

and if (–1 < r < 1)

Ž then equation represents a hyperbola.

Question: The equation \(\frac{x^{2}}{1 - r}\)– \(\frac{y^{2}}{1 + r}\)= 1, r \> 1 represents...