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The differential equation for all family of lines which are at a unit distance from the origin is
- a)[(y)-(x(dy/dx))]2=1-(dy/dx)2
- b)[(y)+(x(dy/dx))]2=1+(dy/dx)2
- c)[(y)-(x(dy/dx))]2=1+(dy/dx)2
- d)[(y)+(x(dy/dx))]2=1-(dy/dx)2
Correct answer is option 'C'. Can you explain this answer?
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The differential equation for all family of lines which are at a unit ...
Explanation:
Differential equation for family of lines at a unit distance from the origin:
To find the differential equation for the family of lines that are at a unit distance from the origin, we can start by considering the general equation of a straight line passing through the origin:
y = m*x
Here, 'm' is the slope of the line. Since the lines are at a unit distance from the origin, the distance formula from a point (x, y) to the origin (0, 0) should be equal to 1:
sqrt(x^2 + y^2) = 1
Squaring both sides of the equation, we get:
x^2 + y^2 = 1
Differentiating both sides of the equation with respect to 'x', we get:
2*x + 2*y*(dy/dx) = 0
Simplifying the above equation, we get:
y + x*(dy/dx) = 0
Squaring both sides of the equation, we get the final form of the differential equation:
[(y) - x*(dy/dx)]^2 = 1 + (dy/dx)^2
Therefore, the correct option is (c) [(y) - x*(dy/dx)]^2 = 1 + (dy/dx)^2.
Differential equation for family of lines at a unit distance from the origin:
To find the differential equation for the family of lines that are at a unit distance from the origin, we can start by considering the general equation of a straight line passing through the origin:
y = m*x
Here, 'm' is the slope of the line. Since the lines are at a unit distance from the origin, the distance formula from a point (x, y) to the origin (0, 0) should be equal to 1:
sqrt(x^2 + y^2) = 1
Squaring both sides of the equation, we get:
x^2 + y^2 = 1
Differentiating both sides of the equation with respect to 'x', we get:
2*x + 2*y*(dy/dx) = 0
Simplifying the above equation, we get:
y + x*(dy/dx) = 0
Squaring both sides of the equation, we get the final form of the differential equation:
[(y) - x*(dy/dx)]^2 = 1 + (dy/dx)^2
Therefore, the correct option is (c) [(y) - x*(dy/dx)]^2 = 1 + (dy/dx)^2.
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The differential equation for all family of lines which are at a unit distance from the origin isa)[(y)-(x(dy/dx))]2=1-(dy/dx)2b)[(y)+(x(dy/dx))]2=1+(dy/dx)2c)[(y)-(x(dy/dx))]2=1+(dy/dx)2d)[(y)+(x(dy/dx))]2=1-(dy/dx)2Correct answer is option 'C'. Can you explain this answer?
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The differential equation for all family of lines which are at a unit distance from the origin isa)[(y)-(x(dy/dx))]2=1-(dy/dx)2b)[(y)+(x(dy/dx))]2=1+(dy/dx)2c)[(y)-(x(dy/dx))]2=1+(dy/dx)2d)[(y)+(x(dy/dx))]2=1-(dy/dx)2Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The differential equation for all family of lines which are at a unit distance from the origin isa)[(y)-(x(dy/dx))]2=1-(dy/dx)2b)[(y)+(x(dy/dx))]2=1+(dy/dx)2c)[(y)-(x(dy/dx))]2=1+(dy/dx)2d)[(y)+(x(dy/dx))]2=1-(dy/dx)2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The differential equation for all family of lines which are at a unit distance from the origin isa)[(y)-(x(dy/dx))]2=1-(dy/dx)2b)[(y)+(x(dy/dx))]2=1+(dy/dx)2c)[(y)-(x(dy/dx))]2=1+(dy/dx)2d)[(y)+(x(dy/dx))]2=1-(dy/dx)2Correct answer is option 'C'. Can you explain this answer?.
The differential equation for all family of lines which are at a unit distance from the origin isa)[(y)-(x(dy/dx))]2=1-(dy/dx)2b)[(y)+(x(dy/dx))]2=1+(dy/dx)2c)[(y)-(x(dy/dx))]2=1+(dy/dx)2d)[(y)+(x(dy/dx))]2=1-(dy/dx)2Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The differential equation for all family of lines which are at a unit distance from the origin isa)[(y)-(x(dy/dx))]2=1-(dy/dx)2b)[(y)+(x(dy/dx))]2=1+(dy/dx)2c)[(y)-(x(dy/dx))]2=1+(dy/dx)2d)[(y)+(x(dy/dx))]2=1-(dy/dx)2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The differential equation for all family of lines which are at a unit distance from the origin isa)[(y)-(x(dy/dx))]2=1-(dy/dx)2b)[(y)+(x(dy/dx))]2=1+(dy/dx)2c)[(y)-(x(dy/dx))]2=1+(dy/dx)2d)[(y)+(x(dy/dx))]2=1-(dy/dx)2Correct answer is option 'C'. Can you explain this answer?.
Solutions for The differential equation for all family of lines which are at a unit distance from the origin isa)[(y)-(x(dy/dx))]2=1-(dy/dx)2b)[(y)+(x(dy/dx))]2=1+(dy/dx)2c)[(y)-(x(dy/dx))]2=1+(dy/dx)2d)[(y)+(x(dy/dx))]2=1-(dy/dx)2Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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