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If the co-ordinate of the vertex of the parabola whose parametric equation is x = t2 – t + 1 and y = t2 + t + 1, t ∈ R is (a, b) then (2a + 4b) equals
Correct answer is '6'. Can you explain this answer?
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If the co-ordinate of the vertex of the parabola whose parametric equa...
x = t2 – t + 1 .... (1)
y = t2 + t + 1 .... (2)
y – x = 2t & x + y = 2(t2 + 1)
________on elminating 't' we get
⇒ (x + y – 2) = 2(y - x)/22
(x – y)2 = 2(x + y – 2)
Axis : x – y = 0
Tangent at vertex : x + y – 2 = 0
Vertex : (1, 1) = (x, y)
y = t2 + t + 1 .... (2)
y – x = 2t & x + y = 2(t2 + 1)
________on elminating 't' we get
⇒ (x + y – 2) = 2(y - x)/22
(x – y)2 = 2(x + y – 2)
Axis : x – y = 0
Tangent at vertex : x + y – 2 = 0
Vertex : (1, 1) = (x, y)
Most Upvoted Answer
If the co-ordinate of the vertex of the parabola whose parametric equa...
The parametric equation of a parabola can be written in the form x = t^2, y = at + b, where (t, at + b) are the coordinates of a point on the parabola.
To find the vertex of the parabola, we need to find the values of t, a, and b. Given that x = t^2, we can see that t = ±√x.
Substituting this value of t into the equation y = at + b, we get y = a(±√x) + b.
Since we are looking for the vertex of the parabola, we want to find the values of x and y when the slope of the parabola is zero. This occurs at the vertex.
To find the slope of the parabola, we differentiate the equation y = a(±√x) + b with respect to x.
dy/dx = a/(2√x)
Setting this equal to zero, we get a/(2√x) = 0.
This implies that a = 0, which means the parabola is not a function and does not have a vertex.
Therefore, the parabola with the parametric equation x = t^2 does not have a vertex.
To find the vertex of the parabola, we need to find the values of t, a, and b. Given that x = t^2, we can see that t = ±√x.
Substituting this value of t into the equation y = at + b, we get y = a(±√x) + b.
Since we are looking for the vertex of the parabola, we want to find the values of x and y when the slope of the parabola is zero. This occurs at the vertex.
To find the slope of the parabola, we differentiate the equation y = a(±√x) + b with respect to x.
dy/dx = a/(2√x)
Setting this equal to zero, we get a/(2√x) = 0.
This implies that a = 0, which means the parabola is not a function and does not have a vertex.
Therefore, the parabola with the parametric equation x = t^2 does not have a vertex.
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If the co-ordinate of the vertex of the parabola whose parametric equation isx = t2– t + 1 and y = t2+ t + 1, t ∈ R is (a, b) then (2a + 4b) equalsCorrect answer is '6'. Can you explain this answer?
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If the co-ordinate of the vertex of the parabola whose parametric equation isx = t2– t + 1 and y = t2+ t + 1, t ∈ R is (a, b) then (2a + 4b) equalsCorrect answer is '6'. 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 If the co-ordinate of the vertex of the parabola whose parametric equation isx = t2– t + 1 and y = t2+ t + 1, t ∈ R is (a, b) then (2a + 4b) equalsCorrect answer is '6'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the co-ordinate of the vertex of the parabola whose parametric equation isx = t2– t + 1 and y = t2+ t + 1, t ∈ R is (a, b) then (2a + 4b) equalsCorrect answer is '6'. Can you explain this answer?.
If the co-ordinate of the vertex of the parabola whose parametric equation isx = t2– t + 1 and y = t2+ t + 1, t ∈ R is (a, b) then (2a + 4b) equalsCorrect answer is '6'. 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 If the co-ordinate of the vertex of the parabola whose parametric equation isx = t2– t + 1 and y = t2+ t + 1, t ∈ R is (a, b) then (2a + 4b) equalsCorrect answer is '6'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the co-ordinate of the vertex of the parabola whose parametric equation isx = t2– t + 1 and y = t2+ t + 1, t ∈ R is (a, b) then (2a + 4b) equalsCorrect answer is '6'. Can you explain this answer?.
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