Question
Arrangement of the following ellipses in ascending order of the radii of their director circles
P) 4x2 + 9y2 = 36
Q) 3x2 + 4y2 = 12
R) 9x2 + 16y2 = 144
S) x2 + 2y2 = 4
- SQPR
- PRQS
- RPSQ
- QSRP
Hint:
find out the equations of ellipses in standard form.
The correct answer is: SQPR
SQPR
the radii of the given ellipses are :
P : x2/9 + y2/4 = 1 => r = 3
Q: x2/4 + y2/3 = 1 => r = 2
R: x2/16 + y2/9 = 1 => r = 4
S: x2/4 + y2/2 = 1 => r = 2
Hence, ascending order is Q< S< P< R or S< Q< P< R
the radius of director circle is equal to the length of semi major axis.
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