Question 7 of 70intermediate🔧 ApplyShort Answer1 mark

In each of the following Exercises 6 to 9, find the centre and radius of the circles x² + y² - 4x - 8y - 45 = 0

Correct Answer

Centre: (2, 4), Radius: 65\sqrt{65}

Exercise: EXERCISE 10.1 | Q: 7 | (Page 6)
For More Understanding

Explanation

This question tests the student's ability to convert a general form of circle equation to standard form by completing the square. The method shown in Example 3 of the textbook demonstrates this process clearly.

Solution Steps

  1. Step 1: Rearrange the given equation: (x² - 4x) + (y² - 8y) = 45

  2. Step 2: Complete the square for x and y terms: (x² - 4x + 4) + (y² - 8y + 16) = 45 + 4 + 16

  3. Step 3: Write in standard form: (x - 2)² + (y - 4)² = 65

  4. Step 4: Compare with (x - h)² + (y - k)² = r² to get centre (2, 4) and radius 65\sqrt{65}

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