Question

The equation of the tangent to the parabola $y=2+4x-4x^2$ with slope $-4$ is

• A. $4x+y-6=0$
• B. $4x+y+6=0$
• C. $4x-y-6=0$
• D. $Noneofthese$

Answer 1

The correct option is A $4x+y-6=0$

$y=2+4x-{4x}^2$

$\Rightarrow y=-({4x}^2-4x+1-1)+2$

$\Rightarrow y=-{(2x-1)}^2+3$

$\Rightarrow (y-3)=-4{(x-1/2)}^2$

Slope of the tangent of a certain point on the parabola is $-4$

$\therefore$ $\frac{dy}{dx}=-4$

$\Rightarrow 4-8x=-4$

$\Rightarrow 8x=8$

$x=1$

$\therefore$ $y=2$

$\therefore$ the certain point on the parabola at which the slope of the tangent is $-4$ is $(1,2)$

$\therefore$ equation of the tangent is

$y-2=-4(x-1)$

$\Rightarrow y-2=-4x+4$

$\Rightarrow 4x+y-6=0$

$\therefore$ Answer : Option A.