Q.For the parabola $y^2=12x$, find the coordinates of the focus, the equation of the directrix, and the length of the latus rectum.

For $y^2 = -x$ we get $a = \tfrac14$; a left-opening parabola has directrix $x = a$, giving $4x - 1 = 0$ (option d).

The standard left-opening parabola is

$y^2 = -4ax,$

with vertex at the origin, focus at $(-a, 0)$ and directrix $x = a$.

Compare with $y^2 = -x$:

$4a = 1 \;\Rightarrow\; a = \frac{1}{4}.$

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The double ordinate through the focus of a conic is called the latus rectum.

Some standard conic terms in the Tamil Nadu HSC Business Maths syllabus:

• Double ordinate: a chord of a conic drawn perpendicular to the axis (a chord parallel to the directrix).
• Focal chord: any chord passing through the focus.
• Latus rectum: the double ordinate that passes through the focus — i.e. the focal chord drawn perpendicular to the axis. …