James has two circles, Circle A and Circle B. Use the information to answer the questions that follow. Circle A: The equation for circle A is x2+y2+6x−4y−12=0 Circle B: center (0, −4) with a radius of 3 A) Complete the square in order to find the center and radius of Circle A. Show your work and state the center and radius of the circle. B) Does the point (8, −3) lie on Circle B? Support your answer with evidence graphically or algebraically. C) Are Circle A and Circle B similar? Yes or no and prove your answer.

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James has two circles, Circle A and Circle B. Use the information to answer the questions that follow.  Circle A: The equation for circle A is x2+y2+6x−4y−12=0  Circle B: center (0, −4) with a radius of 3  A) Complete the square in order to find the center and radius of Circle A. Show your work and state the center and radius of the circle.  B) Does the point (8, −3) lie on Circle B? Support your answer with evidence graphically or algebraically.  C) Are Circle A and Circle B similar? Yes or no and prove your answer.

Demi-Leigh Barrera · Accepted Answer

Step 1  a) Circle A x2+y2+6x−4y−12=0  (x2+6x)+(y2−4y)−12=0  (x2+6x+9−9)+(y2−4y+4−4)−12=0  (x+3)2+(y−2)2−25=0  (x+3)2+(y−2)2=25  Centre x+3=0⇒x=−3  y−2=0⇒y=2  r2=25⇒r=5  Centre (−3, 2) radius =5  B) Circle B  Equation (x−0)2+(y+4)2=32=9  Check (8, −3)  (8)2+(−3+4)2=9  8+1=9  ∵ Point (8, −3) Satishfy the equation of circle B hence point (8, −3) lie on Circle B.  C) Circle A and Circle B ore similar (because all circle are of the same shape hence all circle are similar).

James has two circles, Circle A and Circle B. Use the information to a

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