SOLUTION: X=asectheta and y = btantheta are parametric equation of ........ a)hyperbola b) parabola c)ellipse d) circle

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Question 1083798: X=asectheta and y = btantheta are parametric equation of ........
a)hyperbola
b) parabola
c)ellipse
d) circle
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
X = a%2Asec%28theta%29,  Y = b%2Atan%28theta%29   ====>

X = a%2Fcos%28theta%29,  Y = b%2Atan%28theta%29   ====>

X%2Fa = 1%2Fcos%28theta%29,  Y%2Fb = tan%28theta%29  ====>

%28X%2Fa%29%5E2 = 1%2Fcos%5E2%28theta%29,  Y%2Fb%29%5E2 = sin%5E2%28theta%29%2Fcos%5E2%28theta%29  ====>

X%5E2%2Fa%5E2 - Y%5E2%2Fb%5E2 = 1%2Fcos%5E2%28theta%29 - sin%5E2%28theta%29%2Fcos%5E2%28theta%29 = 1.


So, X and Y are constrained by the equation

X%5E2%2Fa%5E2 - Y%5E2%2Fb%5E2 = 1,

which is an equation of hyperbola.