# 37,39

Aakanksha Talreja
34 Points
6 years ago
Image not clear so solution according to what I understand n due to it can’t understand 37th
$39) x=3\cos \theta & y=3sin\theta$
$a=2\cos \phi b=4/3\sin \phi$
$\therefore 4a^{2}x^{2}+9b^{2}y^{2}-12abxy=4(4cos^{2}\phi *9\cos ^{2 }\theta )+9(16/9\sin ^{2}\phi *9\sin ^{2}\theta )-12(8/3\cos \phi \sin \phi *9\cos \theta \sin \theta )$
$=144[\cos ^{2}(\theta +\phi )+(\sin 2\phi *\sin 2\theta)/2 ]-72\sin 2\phi *\sin 2\theta$
$=144\cos ^{2}(\theta +\phi) +72\sin 2\theta *\sin 2\phi -72\sin 2\theta *\sin 2\phi =144\cos ^{2}(\theta +\phi )=144$