Its axis of symmetry is parallel to the x-axis, and it passes through the two points $(3,5)$ and $(6,-1)$
2026-03-31 04:00:13.1774929613
Find the equation of the parabola with its vertex on the line $2y-3x=0$?
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Hint 1: Instead of solving for $x$ and $y$, which won't get you anywhere, write $x=a(y-h)^2+v$ and solve for $a$, $h$, and $v$. (Since the axis of symmetry is parallel to the x-axis, the parabola must be in this form.) Then you have your equation.
Hint 2: Note that $(v, h)$ are the coordinates of the vertex (this parabola is not oriented in the "classical" fashion). Since this is on the line $2y-3x=0$, we have the equation $2h-3v=0$. But we're solving for three variables, so we need two more equations. Luckily, we have two points...