Maths-
General
Easy
Question
The name of the conic represented by the equation x2 + y2 – 2xy + 20x + 10 = 0 is-
- a hyperbola
- an ellipse
- a parabola
- circle
The correct answer is: a parabola
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 ≠ 0
and, h2 – ab = (–1) – 1 × 1 = 0 
h2 = ab.
Thus, we have
Δ ≠ 0 and h2 = ab.
So, the given equation represents a parabola.
Hence (C) is the correct answer.
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