The equation of a circle is x2 + y2 + 6x + 4y + 10 = 1. What is this equation written in its standard form?
A) (x + 3)2 + (y + 2)2 = 4
B) (x + 6)2 + (y + 4)2 - 4
C) (x + 6)2 + (y + 4)2 = 10
D) (x + 3)2 + (y + 2)2 = 10

Option A: is the equation of the circle

Explanation:

The equation of the circle is

We need to write the equation of the circle in standard form.

Let us subtract 10 from both sides of the equation.

Thus, we have,

Grouping the terms,we have,

Now, we shall complete the square, let us add and subtract the equation by 9 to write the term in the form of

Thus, we have,

Simplifying, we get,

Similarly, we shall complete the square for the term in the form of

Thus, we have,

Simplifying, we get,

Thus, the equation of the circle in standard form is

Hence, Option A is the correct answer.

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!