the parametric representation of a pomt
on the ellipse whose foci are (-1,0) and (7,0) and eccentricity 1/2 is

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the parametric representation of a pomt
on the ellipse whose foci are (-1,0) and (7,0) and eccentricity 1/2
is

Ajanta Trivedi · Accepted Answer

it is given that coordinates of Foci
are S(-1,0) and S'(7,0)
therefore SS' = 2ae
2ae = 7-(-1) = 8
ae = 4
a*1/2 = 4 [it is given that eccentricity e = 1/2
therefore a = 8
since b2=a2(1-e2)b2=82
(1-122)=64*1-14=64*34b2=48⇒b=43
centre of the ellipse is given by -1+72,0+02 i e  3,0
therefore equation of the ellipse is
(x-3)282+y2432=1
therefore parametric representation is
x-3=acosθ=8cosθ⇒x=3+8cosθy-0=bsinθ=43sinθ⇒y=43sinθ

hope this helps you

the parametric representation of a pomton the ellipse whose foci are (-1,0) and (7,0) and eccentricity 1/2 is

the parametric representation of a pomt
on the ellipse whose foci are (-1,0) and (7,0) and eccentricity 1/2 is