Question 3 of 70beginner🔧 ApplyShort Answer1 mark

In each of the following Exercises 1 to 5, find the equation of the circle with centre (1/2, 1/4) and radius 1/12

Correct Answer

(x - 1/2)^2 + (y - 1/4)^2 = 1/144

Exercise: EXERCISE 10.1 | Q: 3 | (Page 6)
For More Understanding

Explanation

The context provides the standard equation of a circle with centre (h, k) and radius r as (x - h)^2 + (y - k)^2 = r2r^{2}. Following the method shown in Example 2, we substitute the given centre coordinates and radius directly into this formula.

Solution Steps

  1. Step 1: Identify the given values: centre (h, k) = (1/2, 1/4) and radius r = 1/12.

  2. Step 2: Write the standard equation of the circle: (x - h)^2 + (y - k)^2 = r2r^{2}.

  3. Step 3: Substitute the values into the formula: (x - 1/2)^2 + (y - 1/4)^2 = (1/12)^2.

  4. Step 4: Calculate the square of the radius: (1/12)^2 = 1/144.

  5. Step 5: Write the final equation: (x - 1/2)^2 + (y - 1/4)^2 = 1/144.

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