Mathematics

Problem

For the curve

y^{2} = x^{2} + 4\lambda x

with

\lambda>0

, the tangent at the point whose

x

-coordinate is

1

passes through the fixed point

(0,-3)

. Find the value of

\lambda

. a)

3\sqrt{10}

\dfrac{9}{2}

\dfrac{9+3\sqrt{10}}{2}

\dfrac{3+\sqrt{6}}{2}