Question 37 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: Vertices (± 5, 0), foci (± 4, 0)

Correct Answer

Since the vertices are at (±5, 0), the major axis lies along the x-axis. Hence, the equation of the ellipse is of the form x²/a² + y²/b² = 1.

Given vertices (±5, 0), we have a = 5. Given foci (±4, 0), we have c = 4. Using the relation c² = a² – b², we get: 16 = 25 – b² b² = 9

Therefore, the equation of the ellipse is x²/25 + y²/9 = 1.

Exercise: EXERCISE 10.3 | Q: 10 | (Page 20)
For More Understanding

Explanation

This question follows the same pattern as Example 11 in the textbook. The key steps are: (1) identify that the major axis is on the x-axis since vertices have coordinates (±5, 0), (2) determine a = 5 from vertices and c = 4 from foci, (3) use the fundamental ellipse relation c² = a² – b² to find b² = 9, and (4) write the standard form equation.

Solution Steps

  1. Step 1: Identify that vertices (±5, 0) on x-axis means major axis is horizontal, so equation is x²/a² + y²/b² = 1

  2. Step 2: From vertices, a = 5; from foci, c = 4

  3. Step 3: Apply c² = a² – b² → 16 = 25 – b² → b² = 9

  4. Step 4: Write equation: x²/25 + y²/9 = 1

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