(iv)ax-ay=2,(a-1)x+(a+1)y=2(a^(2)+1)

H.C.F in these polynomial y^(2)-ay-(a+1) and ay^(2)-y-(a+1)

{:(ax + by = 1),(bx + ay = ((a + b)^(2))/(a^(2) + b^(2))-1):}

{:(ax + by = 1),(bx + ay = ((a + b)^(2))/(a^(2) + b^(2))-1):}

If y= e^(ax) sin bx then show that, y_(2)- 2ay_(1) + (a^(2) + b^(2))y= 0

At the point (x_(1),y_(1)) on the curve x^(3)+y^(3)=3axy show that the tangent is (x_(1)^(2)-ay_(1))x+(y_(1)^(2)-ax_(1))y=ax_(1)y_(1)

If area bounded by the curves x=ay^(2) and y=ax^(2) is 1, then a= ______ (agt0)

prove that |{:((a-x)^(2),,(a-y)^(2),,(a-z)^(2)),((b-x)^(2),,(b-y)^(2),,(b-z)^(2)),((c-x)^(2),,(c-y)^(2),,(c-z)^(2)):}| |{:((1+ax)^(2),,(1+bx)^(2),,(1+cx)^(2)),((1+ay)^(2),,(1+by)^(2),,(1+cy)^(2)),((1+az)^(2),,(1+bx)^(2),,(1+cz)^(2)):}| =2 (b-c)(c-a)(a-b)xx (y-z) (z-x)(x-y)