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# Find the equation of the parabola that satisfies the given conditions: Vertex (0, 0) passing through (5, 2) and symmetric with respect to y - axis.

**Solution:**

Since the vertex is (0, 0) and the parabola is symmetric about the y - axis,

the equation of the parabola is either of the form x^{2} = 4ay or x^{2} = - 4ay

The parabola passes through points (5, 2), which lies in the first quadrant.

Therefore,

the equation of the parabola is of the form x^{2} = 4ay, while point (5, 2) must satisfy the equation x^{2} = 4ay

Hence,

⇒ 5^{2} = 4a × 2

⇒ 25 = 8a

⇒ a = 25/8

Thus, the equation of the parabola is

⇒ x^{2} = 4 × 25/8 × y

⇒ x^{2} = 25/2 y

⇒ 2x^{2} = 25 y

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.2 Question 12

## Find the equation of the parabola that satisfies the given conditions: Vertex (0, 0) passing through (5, 2) and symmetric with respect to y-axis.

**Summary:**

The equation of the parabola is 2x^{2} = 25 y

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