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Parabola

The vertex of...

Question

The vertex of a parabola is the point $(a, b)$ and latus rectum is of the length $l .$ If the parabola is upward opening and its axis is parallel to the $y -$ axis, then its equation is

(x + a)^{2} = l (y - b)

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(x - a)^{2} = l (y - b)

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(x + a)^{2} = \frac{l}{2} (y - b)

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(x - a)^{2} = \frac{l}{4} (y - b)

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Solution

The correct option is B $(x - a)^{2} = l (y - b)$
Parabola having axis parallel to $y -$ axis is
$(x - a)^{2} = 4 A (y - b)$ .
According to question, length of latus rectum $4 A = l$ .
Hence, equation of parabola is
$(x - a)^{2} = 4 \times \frac{l}{4} (y - b)$
or $(x - a)^{2} = l (y - b)$

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Parabola

Standard XIII Mathematics

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The vertex of a parabola is the point (a,b) and latus rectum is of the length l. If the parabola is upward opening and its axis is parallel to the y−axis, then its equation is

The correct option is B (x−a)2=l(y−b)Parabola having axis parallel to y−axis is (x−a)2=4A(y−b). According to question, length of latus rectum 4A=l. Hence, equation of parabola is (x−a)2=4×l4(y−b) or (x−a)2=l(y−b)

The vertex of a parabola is the point $(a, b)$ and latus rectum is of the length $l .$ If the parabola is upward opening and its axis is parallel to the $y -$ axis, then its equation is

The correct option is B $(x - a)^{2} = l (y - b)$
Parabola having axis parallel to $y -$ axis is
$(x - a)^{2} = 4 A (y - b)$ .
According to question, length of latus rectum $4 A = l$ .
Hence, equation of parabola is
$(x - a)^{2} = 4 \times \frac{l}{4} (y - b)$
or $(x - a)^{2} = l (y - b)$