Question

Which equation represents a circle with the same radius as the circle shown but with a center at (-1, 1)? (x – 1)2 + (y + 1)2 = 16 (x – 1)2 + (y + 1)2 = 4 (x + 1)2 + (y –1)2 = 4 (x + 1)2 + (y – 1)2 = 16

Answer 1

(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:

$\boxed{\boxed{ \ (x - h)^2 + (y - k)^2 = r^2 \ }}$

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.

$\boxed{ \ (x - (-1))^2 + (y - 1)^2 = 4^2 \ }$

$\boxed{ \ (x + 1)^2 + (y - 1)^2 = 4^2 \ }$

As result, the equation is $\boxed{\boxed{ \ (x + 1)^2 + (y - 1)^2 = 16 \ }}$

$\boxed{ \ Option \ D \ }$

Note:

$\boxed{ \ (x + 1)^2 + (y - 1)^2 = 16 \ }$

Expand the equation, implement the square of the binomial pattern.

$\boxed{ \boxed{ \ (a + b)^2 = a^2 +2ab + b^2 \ } }$

$\boxed{ \ x^2 + 2x + 1 + y^2 - 2y + 1 = 16 \ }$

Rearrange the equation.

$\boxed{ \ x^2 + y^2 + 2x - 2y + 1 +1 - 16 = 0 \ }$

Once more, we get the general form of the equation of the given circle  $\boxed{\boxed{ \ x^2 + y^2 + 2x - 2y - 14 = 0 \ }}$

Learn more

1. What is the general form of the equation of the given circle with center A(-3,12) and the radius is 5? brainly.com/question/1506955
2. The piecewise-defined functions brainly.com/question/9590016
3. The midpoint brainly.com/question/3269852

Keywords: which equation represents, a circle, with the same radius, shown, center

Answer 2

Answer:

(x + 1)² + (y -1)² = 16

Step-by-step explanation:

just did it on edge