An ellipse is drawn by taking a diameter of thec circle $${\left( {x - 1} \right)^2} + {y^2} = 1$$ as its semi-minor axis and a diameter of the circle $${x^2} + {\left( {y - 2} \right)^2} = 4$$ 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
$$4{x^2} + {y^2} = 4$$
B
$${x^2} + 4{y^2} = 8$$
C
$$4{x^2} + {y^2} = 8$$
D
$${x^2} + 4{y^2} = 16$$
Explanation
Equation of circle is $${\left( {x - 1} \right)^2} + {y^2} = 1$$
$$ \Rightarrow $$ radius $$=1$$ and diameter $$=2$$
$$\therefore$$ Length of semi-minor axis is $$2.$$
Equation of circle is $${x^2} + {\left( {y - 2} \right)^2} = 4 = {\left( 2 \right)^2}$$
$$ \Rightarrow $$ radius $$=2$$ and diameter $$=4$$