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in Parabola by (53.1k points)

Find equation of the parabola given that its vertex is (0,0) axis is Y-axis and passed through (-1,-3).

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Given v = (0,0) and axis is y-axis 

The parabola is of the form x2 = 4ay or x2 = -4ay 

But this equation passes through (-1,-0) which is in III qhadrant. 

∴ The curve turn down words and is of the form x2 = – 4ay, 

But it passes through (-1,-3) 

∴ (-1)2 = -4a(-3) ⇒ 1 = 12a ⇒ a = \(\frac{1}{12}\)

∴ The required equation is x2 = -4 . \(\frac{1}{12}\) y 

⇒ x2 = \(\frac{-1}{3}\) or 3x2 + y = 0

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