Question 18 of 70beginner🔧 ApplyShort Answer2 marks

In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum: y² = -8x

Correct Answer

The given equation is y² = -8x.

Comparing with the standard form y² = 4ax, we get 4a = -8, so a = -2. Since the coefficient of x is negative, the parabola opens to the left.

Focus: (-2, 0)

Axis of the parabola: x-axis

Equation of directrix: x = 2

Length of latus rectum: 8

Exercise: EXERCISE 10.2 | Q: 3 | (Page 11)
For More Understanding

Explanation

This question is from Exercise 10.2, Question 3. The standard form y² = 4ax is used for comparison. When the coefficient of x is negative (as in y² = -8x), the parabola opens to the left. The focus shifts to (-a, 0), the directrix becomes x = -a (which equals x = 2 since a = -2), and the latus rectum length remains |4a| = 8.

Solution Steps

  1. Step 1: Compare y² = -8x with standard form y² = 4ax to get 4a = -8, hence a = -2

  2. Step 2: Identify focus as (a, 0) = (-2, 0)

  3. Step 3: Identify axis as x-axis since equation involves y²

  4. Step 4: Find directrix as x = -a = -(-2) = 2

  5. Step 5: Calculate latus rectum length as 4|a| = 4×24 \times 2 = 8

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