Question

what is the value of b x^2+y^2+ax+by+c=0

Answer 1

the value of \(b\) for what?

Answer 2

for that equation, \[x ^{2}+y ^{2^{}}+ax+by+c=0\]

Answer 3

@helder_edwin

Answer 4

r u sure the question is exactly that?

it kind of doesn't make sense

Answer 5

this graph is part of the question

Answer 6

u also need to find the values of a, b, and c so that the equation describes the circle of the figure.

complete both squares. u know the center and the radius of the circle (see the graph)

Answer 7

that doesnt help me

Answer 8

but thanks

Answer 9

do u know how to complete the square?

Answer 10

no

Answer 11

ok i will do it.

first the center is C(-2,1) and r=3, do u agree?

Answer 12

yes

Answer 13

I got that far.

Answer 14

ok know, the equation of a circle should be
\[\large (x-h)^2+(y-k)^2=r^2 \]

we have to make the equation
\[\large x^2+y^2ax+by+c=0 \]
to resemble this. OK?

Answer 15

\[\large x^2+y^2+ax+by+c=0 \]

Answer 16

(x+2)^2+(y-1)^2=3^2

Answer 17

we know that h=-2, k=1, and r=3, agree?

Answer 18

yes. expand that!

Answer 19

can u do it?

Answer 20

(x+2)+(x+2)+(y-1)+(y-1)=9?

Answer 21

I'm so confuseddd.

Answer 22

no
\[\large (x+2)^2+(y-1)^2=3^2 \]
\[\large (x^2+4x+4)+(y^2-2x+1)=9 \]
\[\large x^2+y^2+4x-2y+5=9 \]
\[\large x^2+y^2+4x-2y-4=0 \]

Answer 23

got it?

Answer 24

so b is 4?

Answer 25

no, b is the coefficient of \(y\)

Answer 26

oh -2?

Answer 27

yes

Answer 28

can you help me with this one?

Answer 29

same question?

Answer 30

have to find a now. so the center is (-1,3) and radius is 4 right?

Answer 31

(x+1)+(y-3)=16?

Answer 32

correction number one, the centre of circle is (1,-2) not (-2,1).
so, h = 1 and k = -2

now remember the equation of circle is
x^2 + y^2 +ax + by + c = 0 or
(x - h)^2 + (y -k)^2 = 0
h,k is the centre of circle.
the relation of b and k is
b = -1/2(k)

so, b = -1/2(-2) = 1

Answer 33

YES. I am so sorry, my mistake.

Answer 34

oh boy. okay.

Answer 35

in the second case the center is (3,-1) and r=4

Answer 36

correction again, im not a boy, but a father of that boy ;p

Answer 37

does A have a certain formula that can be used to find it?

Answer 38

dont learn formulas, learn concepts. do what i did before: expand
\[\large (x-3)^2+(y+1)^2=4^2 \]
it should take a minute

Answer 39

Welcome To Openstudy

Answer 40

a = -1/2 * h

Answer 41

so (x^2-6x+9)+(y^2+2x+1)=16?

Answer 42

so a would be = -3 1/2

Answer 43

a=-6, that is what u got.

Answer 44

It should be (x^2-6x+9)+(y^2+2y+1)=16 (you had 2x, it should be 2y).

In bx^2+y^2+ax+by+c=0, a is the coefficient of x.
The coefficient of x in the equation you got is -6
So a = -6.