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

Solution:

Since the vertex is (0, 0) and the axis of the parabola is the x-axis,

the equation of the parabola is either of the form y² = 4ax or y² = - 4ax

The parabola passes through points (2, 3), which lies in the first quadrant.

Therefore,

the equation of the parabola is of the form y² = 4ax,

while point (2, 3) must satisfy the equation y² = 4ax

Hence,

3² = 4a × 2

⇒ a = 9 / 8

Thus, the equation of the parabola is

⇒ y² = 4 × 9/8 × (x)

⇒ y² = 9/2 x

⇒ 2y² = 9x

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NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.2 Question 11

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

Summary:

The equation of the parabola is 2y² = 9x