[+2b,(" vi) "(x)/(a)+(y)/(b)=2],[+b,quad ax-by=a^(2)-b^(2)]

Solve: (x)/(a)+(y)/(b)=2,quad ax-by=a^(2)-b^(2)

x+y=a+b,ax-by=a^(2)-b^(2)

Solve for xandy: (x)/(a)+(y)/(b)=2,ax-by=a^(2)-b^(2)

(x)/(a)-(y)/(b)=0,ax+by=a^(2)+b^(2)

{:(x + y = a + b),(ax - by = a^(2) - b^(2)):}

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 2a=b, the pair of equations ax+by=2a^(2)-3b^(2),x+2y=2a-6b possess

Solve for x and y. (a-b)x+(a+b)y=a^(2)-2ab-b^(2) , (a+b)(x+y)=a^(2)+b^(2)