The eccentricity of the ellipse `3x^2+4y^2=12` is decreasing at the rate of 0.1 per sec.The time at which it will coincide with auxiliary circle is:

Options

A. 2 seconds
B. 3 seconds
C. 5 seconds
D. 6 seconds

Answer

C

Explanation

Eccentricity of ellipse `=(1)/(2)`
`(de)/(dt)=-0.1" (given)"`
Eccentricity of auxiliary circle = 0
`rArr" "int_(1//2)^(0)de=-0.1 int_(0)^(T)dt`
T is time at which it will touch the auxiliary circle.
`rArr" "-(1)/(2)=-0.1 (T-0)" "thereforeT=5 " seconds."`