(x + 1)² + (y -1)² = 16
Further explanation
The original question is presented in the attached picture.
The circle radius on the graph represents 4 units. Let's find a circle with the same radius as the circle shown but with a center (-1, 1).
The formula for the equation of a circle is as follows:
[tex]\boxed{\boxed{ \ (x - h)^2 + (y - k)^2 = r^2 \ }}[/tex]
This is also called the standard equation of a circle.
- The center is at (h, k)
- The radius represent r (in units)
Let's substitute (h, k) = (-1, 1) and r = 4 into the formula.
[tex]\boxed{ \ (x - (-1))^2 + (y - 1)^2 = 4^2 \ }[/tex]
[tex]\boxed{ \ (x + 1)^2 + (y - 1)^2 = 4^2 \ }[/tex]
As result, the equation is [tex]\boxed{\boxed{ \ (x + 1)^2 + (y - 1)^2 = 16 \ }}[/tex]
[tex]\boxed{ \ Option \ D \ }[/tex]
Note:
[tex]\boxed{ \ (x + 1)^2 + (y - 1)^2 = 16 \ }[/tex]
Expand the equation, implement the square of the binomial pattern.
[tex]\boxed{ \boxed{ \ (a + b)^2 = a^2 +2ab + b^2 \ } }[/tex]
[tex]\boxed{ \ x^2 + 2x + 1 + y^2 - 2y + 1 = 16 \ }[/tex]
Rearrange the equation.
[tex]\boxed{ \ x^2 + y^2 + 2x - 2y + 1 +1 - 16 = 0 \ }[/tex]
Once more, we get the general form of the equation of the given circle [tex]\boxed{\boxed{ \ x^2 + y^2 + 2x - 2y - 14 = 0 \ }}[/tex]
Learn more
- What is the general form of the equation of the given circle with center A(-3,12) and the radius is 5? https://brainly.com/question/1506955
- The piecewise-defined functions https://brainly.com/question/9590016
- The midpoint https://brainly.com/question/3269852
Keywords: which equation represents, a circle, with the same radius, shown, center
