Question

Find the equation of a circle with centre at (5, - 1) and radius 2 units ?
1. x2 + y2 - 10x + 2y - 22 = 0
2. x2 + y2 - 10x + 2y + 22 = 0
3. x2 + y2 + 10x + 2y + 22 = 0
4. x2 + y2 + 10x - 2y + 22 = 0

Answer 1

Correct Answer - Option 2 : x2 + y2 - 10x + 2y + 22 = 0

Concept:

Equation of circle with centre at (h, k) and radius r units is given by: (x - h)2 + (y - k)2 = r2

Calculation:

Here, we have to find the equation of a circle with centre at (5, - 1) and radius 2 units.

As we know that, the equation of circle with centre at (h, k) and radius r units is given by: (x - h)2 + (y - k)2 = r2

Here, we have h = 5, k = - 1 and r = 2

So, the equation of the required circle is: (x - 5)2 + (y + 1)2 = 22

⇒ x2 - 10x + 25 + y2 + 2y + 1 = 4

⇒ x2 + y2 - 10x + 2y + 22 = 0

So, the required equation of circle is x2 + y2 - 10x + 2y + 22 = 0

Hence, option 2 is the correct answer.