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Th e curve described par ametr ically by x = t2 + t + 1, y = t2 – t + 1 represents (1999 - 2 Marks)
- a)a pair of straight lines
- b)an ellipse
- c)a parabola
- d)a hyperbola
Correct answer is option 'C'. Can you explain this answer?
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KEY CONCEPT
The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents a parabola if Δ ≠ 0 and h2 = ab where Δ = abc + 2fgh – af 2 – bg2 – ch2
Now we have x = t2 + t + 1 and y = t2 – t + 1
The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents a parabola if Δ ≠ 0 and h2 = ab where Δ = abc + 2fgh – af 2 – bg2 – ch2
Now we have x = t2 + t + 1 and y = t2 – t + 1
(Adding and subtracting values of x and y)Eliminating t, 2 (x + y) = (x – y)2 + 4 ......... (1)
⇒ x2 – 2xy + y2 – 2x – 2y + 4 = 0 ......... (2)
Here, a = 1, h = – 1, b = 1, g = – 1, f = – 1, c = 4
∴Δ ≠ 0. and h2 = ab
Hence the given curve represents a parabola.
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Th e curve described par ametr ically by x = t2 + t + 1, y = t2 – t + 1 represents (1999 - 2 Marks)a)a pair of straight linesb)an ellipsec)a parabolad)a hyperbolaCorrect answer is option 'C'. Can you explain this answer?
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