If a parabola passing through point $(- 4, - 2)$ has its vertex at the origin and $y -$ axis as its axis of symmetry, then the length of the latus rectum of the parabola is

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Solution

Since the parabola has its vertex at the origin and $y -$ axis as its axis of symmetry and also passes through point $(- 4, - 2)$ ,
so, the equation of parabola will be in the form $x^{2} = - 4 a y$
Since parabola passes through point $(- 4, - 2),$
$∴ (- 4)^{2} = - 4 a (- 2)$
$\Rightarrow a = 2$
Length of the latus rectum $= 4 a = 8$

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Length of Latus Rectum

Standard XII Mathematics

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If a parabola passing through point (−4,−2) has its vertex at the origin and y−axis as its axis of symmetry, then the length of the latus rectum of the parabola is

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If a parabola passing through point $(- 4, - 2)$ has its vertex at the origin and $y -$ axis as its axis of symmetry, then the length of the latus rectum of the parabola is