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Question
Find the equation of a parabola with vertex at the origin, the axis along x-axis and passing through (2, 3).
Solution
Let the equation of the required parabola be \[y^2 = 4ax\]
Since (1) passes through (2, 3), we have:
\[9 = 4a\left( 2 \right) \Rightarrow a = \frac{9}{8}\]
Thus, the required equation is \[y^2 = \frac{4\left( 9 \right)x}{8}\] i.e. \[2 y^2 = 9x\]
Let the equation of the required parabola be \[y^2 = - 4ax\]
Since (2) passes through (2, 3), we have:
\[9 = - 4a\left( 2 \right) \Rightarrow a = \frac{- 9}{8}\]
Thus, the required equation is \[y^2 = \frac{- 4\left( - 9 \right)x}{8}\] i.e. \[2 y^2 = 9x\]
Hence, in either case, the required equation of the parabola is \[2 y^2 = 9x\]
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