Mathematics

Problem

The curve

x^{2} + \lambda xy + y^{2} = 29

is cut by the vertical line

x = 4

at a point

(4,y_{1})

. If the tangent to the curve at this point is perpendicular to the line

y = x

, determine

\lambda

. a)

\dfrac{3}{16}

-\dfrac{3}{8}

-\dfrac{3}{16}

-\dfrac{16}{3}