" (a) "a^(2)+b^(2)=1

If the tangent to the curve y=sin x, at the point (a,b) on it,passes through the origin, then (i) a^(2)(1+b^(2))=b^(2)( ii) a^(2)(1-b^(2))=b^(2) (iii) b^(2)(1+a^(2))=a^(2)( iv )a^(2)+b^(2)=1

Slope of the common tangent to the ellipse (x^(2))/(a^(2)+b^(2))+(y^(2))/(b^(2))=1,(x^(2))/(a^(2))+(y^(2))/(a^(2)+b^(2))=1 is

28) If a^(2)+b^(2)=1,m^(2)+n^(2)=1, then

which one of the following is the common tangent to the ellipses,(x^(2))/(a^(2)+b^(2))+(y^(2))/(b^(2))=1 and (x^(2))/(a^(2))+(y^(2))/(a^(2)+b^(2))=1?

1+a^(2)-b^(2),2ab,-2b2ab,1-a^(2)+b^(2),2a2b,-2a,1-a^(2)-b^(2)]|=(1+a^(2)+b^(2))^(3)

Show that |{:(1+a^(2)-b^(2),,2ab,,-2b),(2ab,,1-a^(2)+b^(2),,2a),(2b,,-2a,,1-a^(2)-b^(2)):}| = (1+a^(2) +b^(2))^(3)

Show that |{:(1+a^(2)-b^(2),,2ab,,-2b),(2ab,,1-a^(2)+b^(2),,2a),(2b,,-2a,,1-a^(2)-b^(2)):}| = (1+a^(2) +b^(2))^(3)

|(1+a^(2)-b^(2), 2ab, -2b),(2a, 1 -a^(2)+b^(2),2a),(2b, -2a, 1-a^2-b^2)|=(1 + a^2 + b^2)^(3) .