What is the focal distance of a point (x_1, y | vedclass

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(A) The given equation of the parabola is $y^2 = 12x$.Comparing this with the standard form $y^2 = 4ax$,we get $4a = 12$,which implies $a = 3$.The foc

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$x_1 + 3$

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(A) The given equation of the parabola is $y^2 = 12x$.Comparing this with the standard form $y^2 = 4ax$,we get $4a = 12$,which implies $a = 3$.The focus of the parabola $y^2 = 4ax$ is $(a, 0)$,so the focus here is $(3, 0)$.The focal distance of any point $(x_1, y_1)$ on the parabola $y^2 = 4ax$ is given by the formula $|x_1 + a|$.Substituting the value of $a = 3$,the focal distance is $|x_1 + 3|$.Since the point $(x_1, y_1)$ lies on the parabola $y^2 = 12x$,$x_1$ must be greater than or equal to $0$,so $x_1 + 3$ is always positive.Thus,the focal distance is $x_1 + 3$.

List-$I$ (Geometric Property)	List-$II$ (Coordinates/Equations)
$I$. Vertex	$A$. $\left(-\frac{3}{2}, -3\right)$
$II$. Focus	$B$. $\left(\frac{3}{2}, -3\right)$
$III$. Equation of the directrix	$C$. $2x + 5 = 0$
$IV$. Equation of the axis	$D$. $2x + y + 3 = 0$
	$E$. $y + 3 = 0$
	$F$. $(-2, -3)$

What is the focal distance of a point $(x_1, y_1)$ on the parabola $y^2 = 12x$?

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