Question
The parametric representation of a point on the ellipse whose foci are (– 1, 0) and (7,0) and eccentricity 1/2 is-
- (3 + 8 cos θ, 4
sin θ)
- (8 cos θ, 4 sin θ)
- (3 + 4 cos θ, 8 sin θ)
- None of these
sin θ)
sin θ)
cos θ, 8 sin θ)
Hint:
find the equation of the ellipse by using the given parameters . from the equation, find the parametric form of a point on the ellipse
The correct answer is: (3 + 8 cos θ, 4sin θ)
(3 + 8 cos θ, 4sin θ)
Foci are: (-1,0) ,(7,0)
Center of ellipse : ((-1+7)/2,(0+0)/2)=(3,0)
Distance between foci = 7-(-1)= 8 = 2ae
e= ½
a= 8
b=4√3
equation of ellipse :
(x-3)2/64 +(y-0)2/48=1
For an ellipse, x= acos(theta) and y = b sin(theta)
x-3 = 8cos(theta) => x= 3+8cos(theta)
y -0 = 4√3 sin(theta) => y= 4√3 sin(theta)
the parametric form of a point on the ellipse gives us the coordinates of any point on the ellipse for a given angle.
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