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

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(– 2, 2)

(2, – 2)

(– 2, 6)

(2, – 6)

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detailed solution

Correct option is B

4−kx=x−x2 or x2−(k+1)x+4=0 has coincidentroots if (k+1)2−16=0⇒k=3 or −5So x=±2a and the points of contact are (2, – 2)or (– 2, – 6).

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If the line kx+y=4 touches the parabolay=x−x2 then the point of contact is

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