For the circle and the hyperbola :

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

For the circle

x^2 + y^2 = 32

and the hyperbola

xy = 16

: (i) Verify that the point

(4,4)

lies on each curve. (ii) Find the equation of the tangent to each curve at

(4,4)

and hence write the equation of the common tangent.