`x/a+y/b=a+b x/(a^2)+y/(b^2)=2, a!=0, b!=0`

Solve the following pair of equations: (x)/(a)+ (y)/(b)= a +b, (x)/(a^(2)) + (y)/(b^(2))=2, a, b ne 0

x/a-y/b=0 , a x+b y=a^2+b^2

If the origin is shifted to the point ((a b)/(a-b),0) without rotation, then the equation (a-b)(x^2+y^2)-2a b x=0 becomes (A) (a-b)(x^2+y^2)-(a+b)x y+a b x=a^2 (B) (a+b)(x^2+y^2)=2a b (C) (x^2+y^2)=(a^2+b^2) (D) (a-b)^2(x^2+y^2)=a^2b^2

If the origin is shifted to the point ((a b)/(a-b),0) without rotation, then the equation (a-b)(x^2+y^2)-2a b x=0 becomes (A) (a-b)(x^2+y^2)-(a+b)x y+a b x=a^2 (B) (a+b)(x^2+y^2)=2a b (C) (x^2+y^2)=(a^2+b^2) (D) (a-b)^2(x^2+y^2)=a^2b^2

If the origin is shifted to the point ((a b)/(a-b),0) without rotation, then the equation (a-b)(x^2+y^2)-2a b x=0 becomes (A)(a-b)(x^2+y^2)-(a+b)x y+a b x=a^2 (B)(a+b)(x^2+y^2)=2a b (C)(x^2+y^2)=(a^2+b^2) (D)(a-b)^2(x^2+y^2)=a^2b^2

If the pair of lines a x^(2)+2 h x y-a y^(2)=0 and b x^(2)+2 g x y-b y^(2)=0 be such that each bisects the angle between the other then

STATEMENT-1 : The line y = (b)/(a)x will not meet the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1, (a gt b gt 0) . and STATEMENT-2 : The line y = (b)/(a)x is an asymptote to the hyperbola.

STATEMENT-1 : The line y = (b)/(a)x will not meet the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1, (a gt b gt 0) . and STATEMENT-2 : The line y = (b)/(a)x is an asymptote to the hyperbola.

Solve the following system of equations by method of cross-multiplication: (a^2)/x-(b^2)/y=0,\ \ \ (a^2b)/x+(b^2a)/y=a+b ,\ \ \ \ x ,\ y!=0

Solve the following pair of linear equations: (i) p x+q y=p q ;" "q x p y=p+q (ii) a x+b y=c ;" "b x+a y=1+c (iii) x/a-y/b=0 ; a x+b y=a^2+b^2 (iv) (a-b)x+(a+b)y=a^2-2a b-b^2; (a+b)(x+y)=a^2+b^2 (v) 152 x 378 y= 74 ;" " 378