Question

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

• A. $4x^2+y^2=4$
• B. $x^2+4y^2=8$
• C. $4x^2+y^2=8$
• D. $x^2+4y^2=16$

Answer 1

The correct option is D $x^2+4y^2=16$

$(x-1{)}^2+y^2=1$

Radius $=1$

Diameter$=2$

$b=2$

$x^2+(y-2{)}^2=4$

Radius$=\sqrt{4}=2$

Diameter$=4$

$a=4$

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is the equation of ellipse

$\frac{x^2}{4^2}+\frac{y^2}{2^2}=1$

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

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