The length of the latus rectum of the parabola $x^2=24y$ is : (a) $8$ (b) $24$ (c) $6$ (d) $12$

> [!TLDR] > Comparing $x^2=24y$ with the standard form $x^2=4ay$ directly gives the latus rectum length as $24$. > > 1. The standard form of a parabola opening upward is $x^2=4ay$, whose latus rectum has length $4a$. > 2. Comparing the given equation $x^2=24y$ with $x^2=4ay$, we get $4a=24$. …

The length of the latus rectum of the parabola x²=24y is : (a) 8 (b) 24 (c) 6 (d) 12

Question 107 of 126

x^2=24y

(a)

8

(b)

24

(c)

6

(d)

12

Puducherry TnboardTamil Nadu HSC (DGE) Board 2022MCQ· 1mImportance★★★★★

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Concept understanding — Parabola — Standard Equation

Setting eccentricity $e=1$ in the conic definition ( $SP=e\cdot PM$ ) gives the parabola — the locus of points equidistant from a fixed focus and a fixed directrix.

Standard form (vertex at the origin, focus on the axis). With focus $(a,0)$ and directrix $x=-a$ : $y^2=4ax$ (opens right). The other three orientations, by symmetry: $y^2=-4ax$ (left), $x^2=4ay$ (up), $x^2=-4ay$ (down).

Vocabulary. Axis: line through the focus $\perp$ directrix. Vertex: where the axis meets the curve. Focal chord: any chord through the focus. Latus rectum: the focal chord $\perp$ the axis; for $y^2=4ax$ its endpoints are $(a,\pm2a)$ , so its length is $4a$ .

Vertex at $(h,k)$ :

Equation	Focus	Directrix
$(y-k)^2=4a(x-h)$	$(h+a,k)$	$x=h-a$
$(y-k)^2=-4a(x-h)$	$(h-a,k)$	$x=h+a$
$(x-h)^2=4a(y-k)$	$(h,k+a)$	$y=k-a$
$(x-h)^2=-4a(y-k)$	$(h,k-a)$	$y=k+a$

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Comparing $x^2=24y$ with the standard form $x^2=4ay$ directly gives the latus rectum length as $24$ .

The standard form of a parabola opening upward is $x^2=4ay$ , whose latus rectum has length $4a$ .
Comparing the given equation $x^2=24y$ with $x^2=4ay$ , we get $4a=24$ . …

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Q.The length of the latus rectum of the parabola x2=24yx^2=24yx2=24y is :

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Q.The length of the latus rectum of the parabola $x^2=24y$ is :

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