First slide

Parabola

Question

If the line $k x + y = 4$ touches the parabola
$y = x - x^{2}$ then the point of contact is

Moderate

A

(– 2, 2)
B

(2, – 2)
C

(– 2, 6)
D

(2, – 6)

Solution

$4 - k x = x - x^{2} or x^{2} - (k + 1) x + 4 = 0$ has coincident
roots if $(k + 1)^{2} - 16 = 0 \Rightarrow k = 3 or - 5$
So $x = \pm 2 a$ and the points of contact are (2, – 2)
or (– 2, – 6).

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