Question 6 of 70beginner💡 UnderstandShort Answer1 mark

In each of the following Exercises 6 to 9, find the centre and radius of the circles (x + 5)² + (y - 3)² = 36

Correct Answer

The centre of the circle is (−5,3)(-5, 3) and the radius is 66.

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

Explanation

The provided context establishes the standard equation of a circle as (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2, where (h,k)(h, k) is the centre and rr is the radius. This is derived from the solution snippet showing that for the equation (x+3)2+(y−2)2=16(x + 3)^2 + (y - 2)^2 = 16, the centre is (−3,2)(-3, 2) and radius is 44. By comparing the given equation (x+5)2+(y−3)2=36(x + 5)^2 + (y - 3)^2 = 36 with the standard form, we identify the values of hh, kk, and rr.

Solution Steps

  1. Step 1: Identify the standard equation of a circle from the context, which is (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2, where (h,k)(h, k) is the centre and rr is the radius.

  2. Step 2: Compare the given equation (x+5)2+(y−3)2=36(x + 5)^2 + (y - 3)^2 = 36 with the standard form. Rewrite the terms as (x−(−5))2+(y−3)2=62(x - (-5))^2 + (y - 3)^2 = 6^2.

  3. Step 3: Equate the parameters. We find h=−5h = -5, k=3k = 3, and r2=36r^2 = 36.

  4. Step 4: Calculate the radius r=36=6r = \sqrt{36} = 6. Thus, the centre is (−5,3)(-5, 3) and the radius is 66.

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