An ellipse is drawn by taking the length of a diameter of the circle (x-1)2+y2=1 as its semi-minor axis and length of diameter of the circle x2+(y-2)2=4 as its semi-major axis. If the centre of ellipse is at origin and its axes are the coordinate axes, then eccentricity of ellipse is

Question

An ellipse is drawn by taking the length of a diameter of the circle (x-1)2+y2=1 as its semi-minor axis and length of diameter of the circle x2+(y-2)2=4 as its semi-major axis. If the centre of ellipse is at origin and its axes are the coordinate axes, then eccentricity of ellipse is (A) (1/2) (B) (1/√2) (C) (√3/2) (D) (√2/3)

Tardigrade Admin · Accepted Answer

Here, a =4, b =2 ⇒ e 2=1-(4/16)=(12/16)=(3/4) ⇒ e =(√3/2)

$\frac{1}{2}$

$\frac{1}{2}$

$\frac{3}{2}$

$\frac{2}{3}$

Here, $a = 4, b = 2 \Rightarrow e^{2} = 1 - \frac{4}{16} = \frac{12}{16} = \frac{3}{4} \Rightarrow e = \frac{3}{2}$

Q. An ellipse is drawn by taking the length of a diameter of the circle (x−1)2+y2=1 as its semi-minor axis and length of diameter of the circle x2+(y−2)2=4 as its semi-major axis. If the centre of ellipse is at origin and its axes are the coordinate axes, then eccentricity of ellipse is

21​

2​1​

23​​

32​​

Here, a=4,b=2⇒e2=1−164​=1612​=43​⇒e=23​​

$\frac{1}{2}$

$\frac{1}{2}$

$\frac{3}{2}$

$\frac{2}{3}$

Here, $a = 4, b = 2 \Rightarrow e^{2} = 1 - \frac{4}{16} = \frac{12}{16} = \frac{3}{4} \Rightarrow e = \frac{3}{2}$