[(sqrt(x)(i))/(a)+(y)/(b)=2],[ax+by=a^(2)-b^(2)]

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

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

x+y=a+b,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)):}

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

int (ax^(2)-b)(dx)/(x sqrt(c^(2))x^(2) -(ax^(2) + b^(2))^(2)

If x+i y=sqrt((a+i b)/(c+i d)) then (x^(2)+y^(2))^(2)=

Show that the equation of the normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (a sqrt(2),b) is ax+b sqrt(2)y=(a^(2)+b^(2))sqrt(2)