Find the coordinates of the point on the curve $y^{2}=3-4 x$ where tangent is parallel to the line $2 x+y-2=0$.
Given that the curve $y^{2}=3-4 x$ has a point where tangent is $\|$ to the line $2 x+y-2=0$.
Slope of the given line is $-2$
$\because$ the point lies on the curve
$\therefore y^{2}=3-4 x$
$\Rightarrow 2 y \frac{d y}{d x}=-4$
$\Rightarrow \frac{d y}{d x}=\frac{-2}{y}$
Now, the slope of the curve $=$ slope of the line
$\Rightarrow \frac{-2}{y}=-2$
$\Rightarrow y=1$
Putting above value in the equation of the line,
$2 x+1-2=0$
$\Rightarrow 2 x-1=0$
$\Rightarrow x=\frac{1}{2}$
So, the required coordinate is $\left(\frac{1}{2}, 1\right)$.
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