Find the equation of the parabola that satisfies the given conditions: Vertex (0, 0) passing through (2, 3) and axis is along x-axis.

Asked by Pragya Singh | 11 months ago |  58

Solution :-

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 y= 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$$(\dfrac{9}{8})x$$

y$$\dfrac{9}{8}x$$

2y2 = 9x

The equation of the parabola is 2y2 = 9x

Answered by Abhisek | 11 months ago

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