91Ó°ÊÓ

The area of the triangle formed by the tangent to the curve \(y=\frac{8}{4+x^{2}}\) at \(x=2\) and the co-ordinate axes is (a) 2 sq. units (b) 4 sq. units (c) 8 sq. units (d) \(\frac{7}{2}\) sq. units

Minimum distance between two points \(P\) and \(Q\), where \(P\) lies on the parabola \(y^{2}-x+2=0\) and \(Q\) lies on the parabola \(x^{2}-y+2=0\) is (a) \(7 \sqrt{2}\) (b) 4 (c) \(\frac{7}{2 \sqrt{2}}\) (d) None

The triangle formed by the tangent to the curve \(f(x)=x^{2}+b x-b\) at \((1,1)\) and the co-ordinate axes, lies in the first quadrant. If its area is 2 , then the value of \(b\) is (a) \(-1\) (b) 3 (c) \(-3\) (d) \(\overline{1}\)

Find the shortest distance between the curves \(y^{2}=x^{3}\) and \(9 x^{2}+9 y^{2}-30 y+16=0 .\)