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The curve described parametrically by x = t2 + 2t − 1, y = 3t + 5 represents
- a)An ellipse
- b)A hyperbola
- c)A parabola
- d)A circle
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The curve described parametrically byx = t2 + 2t − 1, y = 3t + 5...
Y = t2 + 1is a parabola that opens upwards and has its vertex at (0,1). To see this, we can rewrite the parametric equations as:
x = t(t+2)
y = t2 + 1
Solving for t in terms of x, we get:
t = ( -2 ± √(4x+1) ) / 2
Substituting this expression for t into the equation for y, we obtain:
y = ( -2 ± √(4x+1) ) / 2 + 1
which simplifies to:
y = -1 ± √(4x+1)
This is the equation of a parabola that opens upwards and has its vertex at (0,1), as can be seen from its graph:
x = t(t+2)
y = t2 + 1
Solving for t in terms of x, we get:
t = ( -2 ± √(4x+1) ) / 2
Substituting this expression for t into the equation for y, we obtain:
y = ( -2 ± √(4x+1) ) / 2 + 1
which simplifies to:
y = -1 ± √(4x+1)
This is the equation of a parabola that opens upwards and has its vertex at (0,1), as can be seen from its graph:
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Community Answer
The curve described parametrically byx = t2 + 2t − 1, y = 3t + 5...
Given, x=t2+2t−1 ...(i)
On putting the value of t in Eq. (i), we get
This is an equation of a parabola
On putting the value of t in Eq. (i), we get
This is an equation of a parabola
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The curve described parametrically byx = t2 + 2t − 1, y = 3t + 5representsa)An ellipseb)A hyperbolac)A parabolad)A circleCorrect answer is option 'C'. Can you explain this answer?
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The curve described parametrically byx = t2 + 2t − 1, y = 3t + 5representsa)An ellipseb)A hyperbolac)A parabolad)A circleCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The curve described parametrically byx = t2 + 2t − 1, y = 3t + 5representsa)An ellipseb)A hyperbolac)A parabolad)A circleCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The curve described parametrically byx = t2 + 2t − 1, y = 3t + 5representsa)An ellipseb)A hyperbolac)A parabolad)A circleCorrect answer is option 'C'. Can you explain this answer?.
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