If a & b are the y-intercepts of the graph of the equation x^2 + y ^2 - 6x + 4y - 12 = 0 then a + b equals?

Question

If a & b are the y-intercepts of the graph of the equation x^2 + y ^2 - 6x + 4y - 12 = 0 then a + b equals?
a) 4
b) -4
c) 2
d) -2
how do you solve for this???

Answer 1

have you tried completing the squares? if you do that you'll get this equation (x-3)^2 + (y+2)^2 =25. you do that by rearranging your equation like this first

x^2 -6x + y^2 + 4y =12

for x^2 - 6x, think of a constant to turn it into a perfect square trinomial. you do this by dividing 6 by 2 then raising the quotient to the power of two. rememeber the general equation of a quadratic eqaution(ax^2 + bx +c =0)? generally, to get the constant of the perfect square trinomial you do this (b/2)^2. so your perfect square trinomial in x will now be
x^2 - 6x +9

do the same for y and you get
y^2 + 4y + 4
returning to the original equation, since you added 4 and 9 on the left side to complete the square, you also have to add 4 and 9 on the right side so your new equation will now be

x^2 -6x +9 + y^2 + 4y +4 =25

get the factored form of the x and y trinomials and you get

(x-3)^2 + (y+2)^2 = 25

the definition of the y intercept states that x=0 for all values of y so substituting x=0 to the equation, you get

(y+2)^2 = 16

simplifying it you get

y^2 + 4y -12=0

get the factors of the equation and you get

(y-2)(y+6)=0

so y=2 and y= -6

these are your y intercepts a & b

so a+b= -4

hope this helped

Answer 2

A number a is a y-intercept of the graph of the equation f(x,y)=0 if f(0,a)=0. So, let x=0. Then, the y-intercept must satisfy y^2+4y-12=0, or (y+6)(y-2)=0. Therefore, y=-6, or y=2. These are the two y-intercepts a and b.

Answer 3

to find y-intercept, sub x = 0, then solve the equation.

for this question, 0 + y^2 - 0 + 4y - 12 = 0
so y = -4, 2

-4 + 2 = -2

-2 is the solution of a+b

Answer 4

(x-3)^2+(y+2)^2=25=5^2
radius of the circle is 5 and the x intercepts will be
-2 and 8 and the y intercept will be 3 and -7
a+b=-4

Answer 5

ans. a+b= - 4
i.e. option (b)
x^2 + y^2 -6x +4y - 12=0
This is an equation of a circle.
here put x=0.
you'll get a quadratic equation
y^2+4y-12=0
the roots of this equation are a & b.

since sum of roots of this equation is (-b/a)
answer is option (b).