Answer:
a) 1.
f)6.
d)5.
c)7.
g)3.
e)4.
b)2.
Step-by-step explanation:
putting the steps for rewriting the equation of a circle below in standard form completing the square in order:
Step 1)
a. where 36 is added on both sides of the equation
as it is square of half of 12.
x^2 +12x+36 +y^2 +30y=24+36 ..........(1)
Step 2)
f. where 225 is added on both sides of equation as it is square of half of 30
x^2 +12x+36 +y^2 +30y+225=24+36+225 ............(6)
Step3)
d. adding numbers on r.h.s
x^2 +12x+36 +y^2 +30y+225=285 ............(5)
Step4)
c) Factoring the x values into binomial factors
(x+6)(x+6) +36 +y^2 +30y+225=285 .............(7)
Step5)
g) re-writing x factors as squares
(x+6)^2 +36 +y^2 +30y+225=285 ...............(3)
Step6)
e)Factoring the y values into binomial factors
(x+6)^2 +36 +(y+15)(y+15)=285 ...............(4)
Step7)
b)re-writing x factors as squares
(x+6)^2 +36 +(y+15)^2=285 ...........(2)!
