Question 23 of 70beginner🔧 ApplyShort Answer2 marks

In each of the Exercises 7 to 12, find the equation of the parabola that satisfies the given conditions: Focus (0,-3); directrix y = 3

Correct Answer

x² = -12y

Exercise: EXERCISE 10.2 | Q: 8 | (Page 11)
For More Understanding

Explanation

This question tests understanding of standard parabola equations. The focus (0, -3) lies on the y-axis, making the y-axis the axis of the parabola. Since the directrix y = 3 is above the focus, the parabola opens downward with vertex at origin. The standard form is x² = -4ay where a is the distance from vertex to focus.

Solution Steps

  1. Step 1: Identify the axis of the parabola. Since the focus (0, -3) lies on the y-axis, the y-axis is the axis of the parabola.

  2. Step 2: Find the vertex. The vertex is at the midpoint between focus (0, -3) and directrix y = 3. Midpoint = (0, 0). So vertex is at origin.

  3. Step 3: Determine the value of 'a'. Distance from vertex (0, 0) to focus (0, -3) is a = 3.

  4. Step 4: Determine the direction. Since focus is below the vertex and directrix is above, the parabola opens downward.

  5. Step 5: Write the equation. For parabola opening downward with vertex at origin: x² = -4ay. Substituting a = 3: x² = -4(3)y = -12y.

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