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The order ofthe differential equation of all tangent lines to the parabola y = x2is
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'A'. Can you explain this answer?
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The order ofthe differential equation of all tangent lines to the para...
Sol.[A] The parametric form of the given equation is x = t, y = t2. The equation of any tangent at
t is 2xt = y t2. Differentiating, we get 2t = y1. Putting this value in the equation of tangent, we have 2 x y1/2 = y (y1/2)2 Þ 4xy1 = 4y y12
t is 2xt = y t2. Differentiating, we get 2t = y1. Putting this value in the equation of tangent, we have 2 x y1/2 = y (y1/2)2 Þ 4xy1 = 4y y12
The order of this equation is one.
Most Upvoted Answer
The order ofthe differential equation of all tangent lines to the para...
Y=x² dy/dx= 2x since this equation have no constant therefore we will differentiate this only one time that's why it's order is 1 higest power of derivative.
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The order ofthe differential equation of all tangent lines to the para...
The order of a differential equation represents the highest derivative present in the equation. In this case, we are given the equation of a parabola, y = x^2. To find the order of the differential equation of all tangent lines to this parabola, we need to differentiate the given equation and determine the highest order derivative that appears.
Derivative of y = x^2:
Taking the derivative of both sides with respect to x, we get:
dy/dx = 2x
Differentiating once more, we get:
d^2y/dx^2 = 2
Since the second derivative is a constant value, it means that the highest order derivative in the equation is 1. Therefore, the order of the differential equation of all tangent lines to the parabola y = x^2 is 1.
Explanation:
The equation y = x^2 represents a parabola. Differentiating this equation once gives us the derivative dy/dx = 2x, which represents the slope of the tangent line at any given point on the parabola. Differentiating a second time gives us the second derivative d^2y/dx^2 = 2, which represents the rate of change of the slope of the tangent line.
Since the second derivative is a constant value (2), it means that the slope of the tangent line is not changing with respect to x. This indicates that the tangent lines to the parabola are all straight lines, and the highest order derivative in the equation is 1. Therefore, the order of the differential equation of all tangent lines to the parabola y = x^2 is 1.
In summary, the order of the differential equation of all tangent lines to the parabola y = x^2 is 1.
Derivative of y = x^2:
Taking the derivative of both sides with respect to x, we get:
dy/dx = 2x
Differentiating once more, we get:
d^2y/dx^2 = 2
Since the second derivative is a constant value, it means that the highest order derivative in the equation is 1. Therefore, the order of the differential equation of all tangent lines to the parabola y = x^2 is 1.
Explanation:
The equation y = x^2 represents a parabola. Differentiating this equation once gives us the derivative dy/dx = 2x, which represents the slope of the tangent line at any given point on the parabola. Differentiating a second time gives us the second derivative d^2y/dx^2 = 2, which represents the rate of change of the slope of the tangent line.
Since the second derivative is a constant value (2), it means that the slope of the tangent line is not changing with respect to x. This indicates that the tangent lines to the parabola are all straight lines, and the highest order derivative in the equation is 1. Therefore, the order of the differential equation of all tangent lines to the parabola y = x^2 is 1.
In summary, the order of the differential equation of all tangent lines to the parabola y = x^2 is 1.
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The order ofthe differential equation of all tangent lines to the parabola y = x2isa)1b)2c)3d)4Correct answer is option 'A'. Can you explain this answer?
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The order ofthe differential equation of all tangent lines to the parabola y = x2isa)1b)2c)3d)4Correct answer is option 'A'. Can you explain this answer? for Engineering Mathematics 2024 is part of Engineering Mathematics preparation. The Question and answers have been prepared according to the Engineering Mathematics exam syllabus. Information about The order ofthe differential equation of all tangent lines to the parabola y = x2isa)1b)2c)3d)4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Engineering Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The order ofthe differential equation of all tangent lines to the parabola y = x2isa)1b)2c)3d)4Correct answer is option 'A'. Can you explain this answer?.
The order ofthe differential equation of all tangent lines to the parabola y = x2isa)1b)2c)3d)4Correct answer is option 'A'. Can you explain this answer? for Engineering Mathematics 2024 is part of Engineering Mathematics preparation. The Question and answers have been prepared according to the Engineering Mathematics exam syllabus. Information about The order ofthe differential equation of all tangent lines to the parabola y = x2isa)1b)2c)3d)4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Engineering Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The order ofthe differential equation of all tangent lines to the parabola y = x2isa)1b)2c)3d)4Correct answer is option 'A'. Can you explain this answer?.
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