Question 25 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 (-2,0)

Correct Answer

y² = -8x

Exercise: EXERCISE 10.2 | Q: 10 | (Page 11)
For More Understanding

Explanation

This question tests understanding of standard parabola equations. When the vertex is at origin (0,0) and focus lies on the x-axis, the parabola has its axis along the x-axis. Since the focus (-2,0) lies on the negative x-axis, the parabola opens to the left, making it of the form y² = -4ax. The distance from vertex to focus gives a = 2.

Solution Steps

  1. Step 1: Given vertex (0,0) and focus (-2,0). Since the focus lies on the x-axis, the axis of the parabola is the x-axis.

  2. Step 2: The focus (-2,0) is on the negative x-axis, so the parabola opens to the left. Hence, the equation is of the form y² = -4ax.

  3. Step 3: The distance from vertex to focus is a = 2.

  4. Step 4: Substituting a = 2 in y² = -4ax, we get y² = -4(2)x = -8x.

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