Question

The second degree equation

x² + 4y² + 2x + 16y +13 = 0 represent itself as –

• A. A parabola
• B. A pair of straight line
• C. An ellipse
• D. A hyperbola

Answer 1

Answer: (C)

An ellipse

Answer 2

D = $\left| \begin{matrix} a & h & g \\ h & b & f \\ g & f & c \end{matrix} \right| = \left| \begin{matrix} 1 & 0 & 1 \\ 0 & 4 & 8 \\ 1 & 8 & 13 \end{matrix} \right|$= – 16 ¹ 0

Ž does not represent a pair of straight line.

Again h² = 0 & ab = 4

Ž h² < ab

Ž ellipse.