2.75: Tangents to a quadratic curve

0606/23/O/N/18 — Question 11 · 12 marks

A line with equation

y = -5x + k + 5

is a tangent to a curve with equation

y = 7 - kx - x^{2}

(i)

Find the two possible values of

k

[5]

(ii)

Find, for each of your values of

k

, the equation of the tangent, the equation of the curve and the coordinates of the point of contact of the tangent and the curve.

[5]

(iii)

Find the distance between the two points of contact.

[2]