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The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes through the point (4, 3). The equation of the curve is
- a)x2 = y + 5
- b)y2 = x − 5
- c)y2 = x + 5
- d)x2 = y − 5
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The slope of a curve at any point is the reciprocal of twice the ordin...
We have,
Slope = dy/dx ⇒ dy/dx = 1/2y ⇒ 2 y dy = dx
Integrating both sides, we get y2 = x + C
This passes through (4, 3)
∴ 9 = 4 + C ⇒ C = 5
So, the equation of the curve is y2 = x + 5
Slope = dy/dx ⇒ dy/dx = 1/2y ⇒ 2 y dy = dx
Integrating both sides, we get y2 = x + C
This passes through (4, 3)
∴ 9 = 4 + C ⇒ C = 5
So, the equation of the curve is y2 = x + 5
Most Upvoted Answer
The slope of a curve at any point is the reciprocal of twice the ordin...
To find the equation of the curve, we can start by finding the slope of the curve at the point (4, 3).
According to the given information, the slope at any point is the reciprocal of twice the ordinate at the point.
Let's say the ordinate at the point (4, 3) is y. Then, twice the ordinate is 2y. The reciprocal of twice the ordinate is 1/(2y).
So, the slope at the point (4, 3) is 1/(2y).
Now, let's find the value of y at the point (4, 3). Since the point lies on the curve, we can substitute x=4 and y=3 into the equation of the curve.
For option a) y^2 = x - 5:
(3)^2 = 4 - 5
9 = -1
This is not true, so option a) is incorrect.
For option b) y^2 = x:
(3)^2 = 4
9 = 4
This is also not true, so option b) is incorrect.
Therefore, none of the given options are the equation of the curve.
According to the given information, the slope at any point is the reciprocal of twice the ordinate at the point.
Let's say the ordinate at the point (4, 3) is y. Then, twice the ordinate is 2y. The reciprocal of twice the ordinate is 1/(2y).
So, the slope at the point (4, 3) is 1/(2y).
Now, let's find the value of y at the point (4, 3). Since the point lies on the curve, we can substitute x=4 and y=3 into the equation of the curve.
For option a) y^2 = x - 5:
(3)^2 = 4 - 5
9 = -1
This is not true, so option a) is incorrect.
For option b) y^2 = x:
(3)^2 = 4
9 = 4
This is also not true, so option b) is incorrect.
Therefore, none of the given options are the equation of the curve.
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The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes through the point (4, 3). The equation of the curve isa)x2 = y + 5b)y2 = x − 5c)y2 = x + 5d)x2 = y − 5Correct answer is option 'A'. Can you explain this answer?
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The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes through the point (4, 3). The equation of the curve isa)x2 = y + 5b)y2 = x − 5c)y2 = x + 5d)x2 = y − 5Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes through the point (4, 3). The equation of the curve isa)x2 = y + 5b)y2 = x − 5c)y2 = x + 5d)x2 = y − 5Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes through the point (4, 3). The equation of the curve isa)x2 = y + 5b)y2 = x − 5c)y2 = x + 5d)x2 = y − 5Correct answer is option 'A'. Can you explain this answer?.
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