Two circles are concentric if they have the same center. On a coordinate plane, a circle has center (4, 6) and has a r

Question

Two circles are concentric if they have the same center.

On a coordinate plane, a circle has center (4, 6) and has a radius of 2 units.

Which equation represents a circle that is concentric with the circle shown but has a radius that is twice as large?

(x – 4)2 + (y – 6)2 = 4
(x – 4)2 + (y – 6)2 = 16
(x – 6)2 + (y – 4)2 = 16
(x – 6)2 + (y – 4)2 = 4

sori · Answer

The  equation  of the circle is  (x - 4)² + (y - 6)² = 16 . The correct option is the second option  (x - 4)² + (y - 6)² = 16     Equation of a circle   From the question, we are to determine the  equation of the circle      The  equation of circle  is given by   (x - h)² + (y - k)² = r²  Where (h, k) is the  center    and r is the  radius      From the given  information ,   The two circles are concentric  ∴ (h , k) =  (4, 6)     But the other circle has a radius that is twice as large   ∴ r = 2 × 2  r =  4      Thus,   The  equation  of the  circle  becomes   (x - 4)² + (y - 6)² = 4²   (x - 4)² + (y - 6)² = 16     Hence, the  equation  which represents a circle that is concentric with the circle shown but has a radius that is twice as large is  (x - 4)² + (y - 6)² = 16 . The correct option is the second option  (x - 4)² + (y - 6)² = 16       Learn more on  Equation of a circle  here: https://brainly.com/question/1506955    #SPJ1

Equation of a circle

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in the xy-plane, the point (- 2, 1) is the center of a circle that has a radius 2. Which of the following is NOT a point on a circ