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The curve represented by x = a (coshθ + sinhθ) , y = b(coshθ − sinhθ) is
- a)A hyperbola
- b)An ellipse
- c)A parabola
- d)A circle
Correct answer is option 'A'. Can you explain this answer?
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The curve represented by x = a (coshθ + sinhθ), y = b(cosh...
(t/a)) and y = b (sinh(t/a)) is called a hyperbolic curve. It is a type of curve that is similar to an ellipse or a parabola, but with different properties.
The hyperbolic curve has two branches that are symmetric about the y-axis. It is defined by the equations:
x = a (cosh(t/a))
y = b (sinh(t/a))
where t is a parameter that ranges from -∞ to ∞. The constants a and b determine the size and shape of the curve.
One important property of the hyperbolic curve is that it has asymptotes, which are lines that the curve approaches but never crosses. The asymptotes are the lines x = ±a and y = ±b.
Another property of the hyperbolic curve is that it is a self-intersecting curve. This means that the curve intersects itself at certain points. The points of intersection are called nodes.
Hyperbolic curves have applications in various fields, including physics, engineering, and mathematics. For example, they can be used to model the shape of a suspended cable or the trajectory of a projectile in a gravitational field. They also have applications in hyperbolic geometry, which is a non-Euclidean geometry that deals with curved spaces.
The hyperbolic curve has two branches that are symmetric about the y-axis. It is defined by the equations:
x = a (cosh(t/a))
y = b (sinh(t/a))
where t is a parameter that ranges from -∞ to ∞. The constants a and b determine the size and shape of the curve.
One important property of the hyperbolic curve is that it has asymptotes, which are lines that the curve approaches but never crosses. The asymptotes are the lines x = ±a and y = ±b.
Another property of the hyperbolic curve is that it is a self-intersecting curve. This means that the curve intersects itself at certain points. The points of intersection are called nodes.
Hyperbolic curves have applications in various fields, including physics, engineering, and mathematics. For example, they can be used to model the shape of a suspended cable or the trajectory of a projectile in a gravitational field. They also have applications in hyperbolic geometry, which is a non-Euclidean geometry that deals with curved spaces.
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The curve represented by x = a (coshθ + sinhθ), y = b(coshθ − sinhθ)isa)A hyperbolab)An ellipsec)A parabolad)A circleCorrect answer is option 'A'. Can you explain this answer?
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