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Ellipse

Section: Mathematics

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Question : 110 of 117

Marks: +1, -0

An ellipse is drawn by taking a diameter of the circle

(x-1)^2+y^2=1

as its semi-minor axis and a diameter of the circle

x^2+(y-2)^2=4

is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is:

$4x^2+y^2=4$
$x^2+4y^2=8$
$4x^2+y^2=8$
$x^2+4y^2=16$

Solution:

Equation of circle is

(x-1)^2+y^2=1

\Rightarrow

radius

=1

and diameter

=2

\therefore

Length of semi-minor axis is 2 .

Equation of circle is

x^2+(y-2)^2=4=(2)^2

\Rightarrow

radius

=2

and diameter

=4

\therefore

Length of semi major axis is 4

We know, equation of ellipse is given by

\;\frac{x^2}{(\text{ Major axis })^2}+\;\frac{y^2}{(\text{ Minor axis })^2}=1

\Rightarrow \;\frac{x^2}{(4)^2}+\;\frac{y^2}{(2)^2}=1

\Rightarrow \;\frac{x^2}{16}+\;\frac{y^2}{4}=1

\Rightarrow x^2+4y^2=16

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