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t ∈ R represents- a)a circle
- b)an ellipse
- c)a hyperbola
- d)a parabola
Correct answer is option 'C'. Can you explain this answer?
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t∈ R representsa)a circleb)an ellipsec)a hyperbolad)a parabolaCor...
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t∈ R representsa)a circleb)an ellipsec)a hyperbolad)a parabolaCor...
P(x,y) = [(et + e-t)/2 , (et - e-t)/2]
(et + e-t)/2 = x --------------------------(1)
(et - e-t)/2 = y --------------------------(2)
Adding (1) & (2)
2et = 2x + 2y
et = x + y
Eq (1) et + e-t = 2x
et + 1/et = 2x
(et)2 + 1 = 2x*et
(x+y)2 + 1 = 2x(x+y)
x2 + y2 + 2xy + 1 = 2x2 + 2xy
x2 + y2 + 1 = 2x2
(x2)/(1)2 - (y2)/(1)2 = 1 {which represents hyperbola equation}
(et + e-t)/2 = x --------------------------(1)
(et - e-t)/2 = y --------------------------(2)
Adding (1) & (2)
2et = 2x + 2y
et = x + y
Eq (1) et + e-t = 2x
et + 1/et = 2x
(et)2 + 1 = 2x*et
(x+y)2 + 1 = 2x(x+y)
x2 + y2 + 2xy + 1 = 2x2 + 2xy
x2 + y2 + 1 = 2x2
(x2)/(1)2 - (y2)/(1)2 = 1 {which represents hyperbola equation}
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