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The curve described parametrically by x = t2 + t + 1, y = t2 - t + 1 represents
- a)a circle
- b)a parabola
- c)an ellipse
- d)a hyperbola
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The curve described parametrically by x = t2 + t + 1, y = t2 - t + 1 r...
x = t2 +t +1andy = t2 -t +1
⇒ x + y - 2 = 2t2 and x - y = 2t
⇒ 2(x + y -2) = (x - y)2 ⇒ x2 + y2 -2xy -2x -2y + 4 = 0
Comparing with the equation
ax2 + 2hxy + by2 + 2gx + 2fy + c = 0,
∴ abc + 2fgh - af2 - bg2 - ch2 ≠ and h2 = ab
⇒ x + y - 2 = 2t2 and x - y = 2t
⇒ 2(x + y -2) = (x - y)2 ⇒ x2 + y2 -2xy -2x -2y + 4 = 0
Comparing with the equation
ax2 + 2hxy + by2 + 2gx + 2fy + c = 0,
∴ abc + 2fgh - af2 - bg2 - ch2 ≠ and h2 = ab
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The curve described parametrically by x = t2 + t + 1, y = t2 - t + 1 representsa)a circleb)a parabolac)an ellipsed)a hyperbolaCorrect answer is option 'B'. Can you explain this answer?
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