Use a rotation of axes to eliminate the xyterm Write an equa

Use a rotation of axes to eliminate the xy-term. (Write an equation in XY-coordinates. Use a rotation angle that satisfies

0 /2.)

241x² + 576xy + 409y² = 40x 30y + 600

241x² + 576xy + 409y² - 40x + 30y - 600=0

comparing with Ax²+Bxy+Cy²+Dx+Ey+F=0

angle to be rotated to remove xy term =

tan(2)=B_/(A-C)

tan(2)=576_/(241-409)

=53.13^o

x=Xcos-Ysin,y=Xsin+Ycos

x=0.6X-0.8Y,y=0.8X+0.6Y

241x² + 576xy + 409y² - 40x + 30y - 600=0

241(0.6X-0.8Y)² + 576(0.6X-0.8Y)(0.8X+0.6Y) + 409(0.8X+0.6Y)² - 40(0.6X-0.8Y) + 30(0.8X+0.6Y) - 600=0

625X²+25Y²+50Y-600=0