We know that the vertex is (0, 0) and the axis of the parabola is the x-axis
The equation of the parabola is either of the from y2 = 4ax or y2 = -4ax.
Given that the parabola passes through point (2, 3), which lies in the first quadrant.
So, the equation of the parabola is of the form y2 = 4ax, while point (2, 3) must satisfy the equation y2 = 4ax.
Then,
32 = 4a(2)
32 = 8a
9 = 8a
a = \( \dfrac{9}{8}\)
Thus, the equation of the parabola is
y2 = 4(\( \dfrac{9}{8}\))x
= \( \dfrac{9x}{2}\)
2y2 = 9x
The equation of the parabola is 2y2 = 9x
Answered by Aaryan | 1 year agoAn equilateral triangle is inscribed in the parabola y2 = 4ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.
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