Question 1 of 70beginner🔧 ApplyShort Answer1 mark

In each of the following Exercises 1 to 5, find the equation of the circle with centre (0, 2) and radius 2

Correct Answer

The equation of a circle with centre (h,k)(h, k) and radius rr is given by (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2.

Given: Centre (h,k)=(0,2)(h, k) = (0, 2) and radius r=2r = 2.

Substituting these values:

(x−0)2+(y−2)2=22(x - 0)^2 + (y - 2)^2 = 2^2

Simplifying the equation:

x2+(y−2)2=4x^2 + (y - 2)^2 = 4

Thus, the required equation of the circle is x2+(y−2)2=4x^2 + (y - 2)^2 = 4.

Exercise: EXERCISE 10.1 | Q: 1 | (Page 6)
For More Understanding

Explanation

The solution applies the standard formula for the equation of a circle, (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2, as derived in the provided text. By substituting the centre coordinates (0, 2) for (h, k) and radius 2 for r, the equation is formed. This follows the methodology shown in Example 1 and Example 2 of the context.

Solution Steps

  1. Step 1: Identify the standard equation of a circle: (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2.

  2. Step 2: Substitute h=0h = 0, k=2k = 2, and r=2r = 2 into the formula.

  3. Step 3: Simplify the expression (x−0)2+(y−2)2=22(x - 0)^2 + (y - 2)^2 = 2^2 to get x2+(y−2)2=4x^2 + (y - 2)^2 = 4.

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