class 12

Math

Calculus

Application of Derivatives

Consider the hyperbola $H:x_{2}−y_{2}=1$ and a circle S with centre $N(x_{2},0)$ Suppose that H and S touch each other at a point $(P(x_{1},y_{1})$ with $x_{1}>1andy_{1}>0$ The common tangent to H and S at P intersects the x-axis at point M. If (l,m) is the centroid of the triangle $ΔPMN$ then the correct expression is (A) $dx_{1}dl =1−3x_{1}1 $ for $x_{1}>1$ (B) $dx_{1}dm =3(x _{1}−1)x_{!} )forx_{1}>1$ (C) $dx_{1}dl =1+3x_{1}1 forx_{1}>1$ (D) $dy_{1}dm =31 fory_{1}>0$