Question 8 of 70intermediate🔧 ApplyShort Answer1 mark

In each of the following Exercises 6 to 9, find the centre and radius of the circles x² + y² - 8x + 10y - 12 = 0

Correct Answer

Centre: (4, -5), Radius: 53\sqrt{53}

Exercise: EXERCISE 10.1 | Q: 8 | (Page 6)
For More Understanding

Explanation

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

Solution Steps

  1. Step 1: Rearrange the given equation by grouping x and y terms: (x² - 8x) + (y² + 10y) = 12

  2. Step 2: Complete the square for both variables: (x² - 8x + 16) + (y² + 10y + 25) = 12 + 16 + 25

  3. Step 3: Rewrite in standard form: (x - 4)² + (y + 5)² = 53

  4. Step 4: Compare with (x - h)² + (y - k)² = r² to get centre (4, -5) and radius 53\sqrt{53}

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