When a standard parabola $y^{2} = 4 a x$ is flipped about y-axis, then what will be the equation of directrix and coordinates of focus of new parabola?

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Solution

On flipping the parabola $y^{2} = 4 a x$ about the $y$ -axis the sign of $x$ -coordinates reverses and the equation becomes $y^{2} = - 4 a x$ .
$\Rightarrow$ Coordinates of focus will change from $(a, 0)$ to $(- a, 0) .$
Also, equation of directrix change from $x = - a$ to $x = a .$

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