Question

Find the equation of a parabola with vertex at the origin, the axis along x-axis and passing through (2, 3).

Answer 1

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 \[2 y^2 = 9x\]