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in Parabola by (58.3k points)

Find the equation of the parabola if its vertex is (0,0), axis is yaxis and passes through (-1,-3).

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Axis is y-axis and vertex is (0, 0).

∴ The parabola is of the form x2 = 4ay and x2 = -4ay. 

Since the parabola passes through the point (-1, -3) and it lies in third quadrant the parabola turns downward. 

It is of the form x2 = 4ay 

but it passes through the point (-1,-3). 

∴ (-1)2 = -4a(3).

⇒ 1 = 12a ⇒ a = \(\frac{1}{12}\) 

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

12x2 + 4y = 0.

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