Question

If the pair of lines $a{x}^2+2(a+b)xy+b{y}^2=0$ lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then-

• A. $3a^2-10ab+3b^2=0$
• B. $3a^2-2ab+3b^2=0$
• C. $3a^2+10ab+3b^2=0$
• D. $3a^2+2ab+3b^2=0$

Answer 1

The correct option is D $3a^2+2ab+3b^2=0$

from given, we have,

the area of one of the sectors is thrice the area of another sector

$B=3A$

$\frac{2\sqrt{x^2-ab}}{a+b}=\tan \theta$

$\frac{2\sqrt{(a+b{)}^2-ab}}{a+b}=1$

$2^2\left[\right(a+b{)}^2-ab]=(a+b{)}^2$

$4a^2+4ab+4b^2=a^2+b^2+2ab$

$3a^2+2ab+3b^2=0$

Hence the required equation