[" 12."2ax+3by=(a+2b)],[" 3"ax+2by=(2a+b)]

Solve the following system of equations by method of cross-multiplication: 2ax+3by=a+2b,quad 3ax+2by=2a+b

(ax)/b-(by)/a=a+b , ax-by=2ab

(ax)/(b)-(by)/(a)=a+b,ax-by=2ab

If 4x ^(2) + 12 xy - 8x + 9 y ^(2) - 12 y = (ax + by) (ax+ by -4), then the value of a ^(2) +b ^(2) is

If a circle passes through the point (a, b) and cuts the circle x^2 + y^2 = 4 orthogonally, then the locus of its centre is (a) 2ax+2by-(a^(2)+b^(2)+4)=0 (b) 2ax+2by-(a^(2)-b^(2)+k^(2))=0 (c) x^(2)+y^(2)-3ax-4by+(a^(2)+b^(2)-k^(2))=0 (d) x^(2)+y^(2)-2ax-3by+(a^(2)-b^(2)-k^(2))=0

If 4x^(2) + 12xy -8x+9y^(2) -12y = (ax+by) (ax+by-4) , then the value of a^(2) +b^(2) is

6(ax+by)=3a+2b&6(bx-ay)=3b-2a

Solve: (x^2-ax)/b+(x^2-bx)/a+(x^2-3ax-3bx)/(a+b)=0 ]

If x = (sqrt(2a + 3b)+sqrt(2a - 3b))/(sqrt(2a + 3b) - sqrt(2a - 3b)) , show that 3bx^(2) - 4ax + 3b = 0 .