Question 24 of 70beginner🔧 ApplyShort Answer2 marks

In each of the Exercises 7 to 12, find the equation of the parabola that satisfies the given conditions: Vertex (0,0); focus (3,0)

Correct Answer

y2y^{2} = 12x

Exercise: EXERCISE 10.2 | Q: 9 | (Page 11)
For More Understanding

Explanation

The problem is solved by identifying the orientation of the parabola based on the position of the focus relative to the vertex, similar to the method used in Example 7 of the provided text. Since the vertex is at the origin and the focus lies on the x-axis, the parabola opens to the right, and its equation takes the standard form y2y^{2} = 4ax. The value of 'a' is determined by the x-coordinate of the focus.

Solution Steps

  1. Step 1: Identify the axis of the parabola. Since the vertex is at (0,0) and the focus is at (3,0), the focus lies on the x-axis. Therefore, the axis of the parabola is the x-axis.

  2. Step 2: Determine the standard equation form. Since the focus is on the x-axis, the equation of the parabola is of the form y2y^{2} = 4ax.

  3. Step 3: Find the value of a. The coordinates of the focus for the parabola y2y^{2} = 4ax are (a, 0). Given that the focus is (3, 0), comparing the coordinates gives a = 3.

  4. Step 4: Formulate the equation. Substituting a = 3 into the standard form y2y^{2} = 4ax, we get y2y^{2} = 4(3)x, which simplifies to y2y^{2} = 12x.

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