What is the length of the latus rectum of the | vedclass

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(B) The given equation is $x = ay^2 + by + c$.We can rewrite this by completing the square for $y$:$x = a(y^2 + \frac{b}{a}y) + c$$x = a(y^2 + \frac{b

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$\frac{1}{|a|}$

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(B) The given equation is $x = ay^2 + by + c$.We can rewrite this by completing the square for $y$:$x = a(y^2 + \frac{b}{a}y) + c$$x = a(y^2 + \frac{b}{a}y + \frac{b^2}{4a^2}) + c - \frac{b^2}{4a}$$x - (c - \frac{b^2}{4a}) = a(y + \frac{b}{2a})^2$$(y + \frac{b}{2a})^2 = \frac{1}{a}(x - (c - \frac{b^2}{4a}))$This is in the standard form $(y - k)^2 = 4p(x - h)$,where $4p = \frac{1}{a}$.The length of the latus rectum is given by $|4p|$.Therefore,the length is $|\frac{1}{a}| = \frac{1}{|a|}$.

What is the length of the latus rectum of the parabola $x = ay^2 + by + c$?

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