MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability
Problem
Consider the circle x2+y2=25 and the rectangular hyperbola xy=12.
(a) Find all the points of intersection of the two curves.
(b) For each point obtained in part (a), compute the slope of the tangent to the circle and the slope of the tangent to the hyperbola.
(c) Hence determine the equation(s) of the line(s) that are common tangents to both curves at their respective points of contact.