Question 44 of 70beginner🔧 ApplyShort Answer2 marks

In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: Foci (± 3, 0), a = 4

Correct Answer

The equation of the ellipse is x²/16 + y²/7 = 1.

Exercise: EXERCISE 10.3 | Q: 17 | (Page 20)
For More Understanding

Explanation

This question tests understanding of ellipse parameters. Since the foci are at (±3, 0) on the x-axis, the major axis lies along the x-axis, and the standard form x²/a² + y²/b² = 1 applies. Given c = 3 and a = 4, students must apply the fundamental relationship c² = a² - b² to find b² = 7.

Solution Steps

  1. Step 1: Since foci are at (±3, 0) on the x-axis, the major axis is along the x-axis. So the equation is of the form x²/a² + y²/b² = 1.

  2. Step 2: Given c = 3 and a = 4.

  3. Step 3: Using the relation c² = a² - b², we get 9 = 16 - b².

  4. Step 4: Therefore, b² = 16 - 9 = 7.

  5. Step 5: Hence, the equation of the ellipse is x²/16 + y²/7 = 1.

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