Question

The name of the conic represented by the equation

x² + y² – 2xy + 20x + 10 = 0 is-

• A. A hyperbola
• B. An ellipse
• C. A parabola
• D. Circle

Answer 1

Answer: (C)

A parabola

Answer 2

On comparing the given equation with the equation

ax² + 2hxy + by² + 2ƒy + c = 0, we have

a = 1, b = 1, h = –1, c = 10, g = 10 and ƒ = 0.

\ abc + 2ƒgh – aƒ² – bg² – ch² = 10 – 100 – 10 = – 100 ¹ 0

and, h² – ab = (–1) – 1 × 1 = 0 ̃ h² = ab.

Thus, we have

D ¹ 0 and h² = ab.

So, the given equation represents a parabola.

Hence (3) is the correct answer.