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The curve represented by x = a (cosh θ + sinh θ), y = b (cosh θ − sinh θ) is
- a)A hyperbola
- b)An ellipse
- c)A parabola
- d)A circle
Correct answer is option 'B'. Can you explain this answer?
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The curve represented by x = a (cosh θ + sinh θ), y = b (c...
T) and y = b (sinh t) is called a hyperbola. It has two branches that are symmetric about the y-axis.
The parameter a represents the distance between the center of the hyperbola and each of its vertices, while b represents the distance between the center and each of its foci.
The equation of the hyperbola can be written in standard form as:
(x/a)^2 - (y/b)^2 = 1
The asymptotes of the hyperbola are the lines y = ±(b/a)x. These lines intersect at the center of the hyperbola, which is the origin in this case.
The hyperbola has many interesting properties, such as its relationship to conic sections and its use in navigation and engineering.
The parameter a represents the distance between the center of the hyperbola and each of its vertices, while b represents the distance between the center and each of its foci.
The equation of the hyperbola can be written in standard form as:
(x/a)^2 - (y/b)^2 = 1
The asymptotes of the hyperbola are the lines y = ±(b/a)x. These lines intersect at the center of the hyperbola, which is the origin in this case.
The hyperbola has many interesting properties, such as its relationship to conic sections and its use in navigation and engineering.
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