Question

Let lengths of semi-major axis, semi-minor axis and distance of focus from the centre of an ellipse are $a$, $b$ and $c$, respectively.
I. When $c=0$, ellipse becomes circle.
II. When $c=a$, ellipse reduces to the line segment $F_1 F_2$ joining the two foci.

• A. Both I and II are true
• B. Only I is true
• C. Only II is true
• D. Both I and II are false

Answer 1

Answer: (A)

I. When $c=0$, both foci merge together with the centre of the ellipse and $a^2=b^2$, i.e., $a=b$, and so the ellipse becomes circle. Thus, circle is a special case of an ellipse

II. When $c=a$, then $b=0$. The ellipse reduces to the line segment $F_1 F_2$ joining the two foci