The circle meets the rectangular hyperbola in the first quadrant

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

The circle

x^{2}+y^{2}=25

meets the rectangular hyperbola

xy=k

in the first quadrant. For which positive value of

k

do the two curves have a common tangent at their point(s) of intersection? (a)

10

(b)

\dfrac{25}{4}

(c)

\dfrac{25}{2}

(d)

5