Question

Please help me to solve the question!​

Answer 1

Answer:  (x - 3)² + (y + 0.5)² = 3.25    →    $(x-3)^2+\bigg(y+\dfrac{1}{2}\bigg)^2=\dfrac{13}{4}$

Step-by-step explanation:

Concentric means they have the same center but different radii.

The equation of a circle is:  (x - h)² + (y - k)² = r²    where

• (h, k) is the center of the circle
• r is the radius of the circle

Complete the square to find the center of the circle

x² - 6x + _____  + y² + y + _____ = 1 + ____ + ____

    ↓                              ↓

-6/2 = -3                    1/2 = 1/2

Equation: (x - 3)² + (y + 1/2)² = r²

Since the circle passes through point (x, y) = (4, -2), input that into the equation to find r².

(x - 3)² +  (y + 1/2)² = r²

(4 - 3)² + (-2 + 1/2)² = r²

  (1)²    +  (-3/2)²    = r²

   1      +     9/4      = r²

                 13/4     = r²

Equation: (x - 3)² + (y + 1/2)² = 13/4    →   $(x-3)^2+\bigg(y-\dfrac{1}{2}\bigg)^2=\dfrac{13}{4}$

In decimal form: (x - 3)² + (y + 0.5)² = 3.25