Find equation of the parabola given that its vertex is (0,0) axis is Y

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

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

Answer»

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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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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