Can someone please help me find the x-intercepts and y-intecepts of this equation. I have the radius, and center but I can't seem to get the intercepts.
x^2+y^2=16x-18y+145=25
Please show work. Thanks!!
sorry that should be
x^2+y^2+16x-18y+145=25
Been up to long working on this. Again I am sorry!!
regroup things a bit to get
x^2+16x+64 + y^2-18y+81 = 25
(x+8)^2 + (y-9)^2 = 25
no wonder you can't find the intercepts. This is a circle at (-8,9) with radius 5. It's too far away from the axes to intercept them!
that's what I got. thanks
To find the x-intercepts and y-intercepts of the equation, you need to set the y-value or x-value equal to zero, respectively.
Given the equation:
x^2 + y^2 = 16x - 18y + 145 = 25
To find the x-intercepts, set y = 0:
x^2 + (0)^2 = 16x - 18(0) + 145 - 25
x^2 = 16x + 120
Now let's solve for x by rearranging the equation:
x^2 - 16x - 120 = 0
This is a quadratic equation, which can be factored or solved using the quadratic formula. Factoring, you get:
(x - 20)(x + 6) = 0
Setting each factor equal to zero gives us the potential x-intercepts:
x - 20 = 0 --> x = 20
x + 6 = 0 --> x = -6
Therefore, the x-intercepts of the equation are x = 20 and x = -6.
To find the y-intercepts, set x = 0:
(0)^2 + y^2 = 16(0) - 18y + 145 - 25
y^2 = -18y + 120
Again, let's solve for y by rearranging the equation:
y^2 + 18y - 120 = 0
Factoring or using the quadratic formula, you get:
(y + 12)(y - 10) = 0
Setting each factor equal to zero gives us the potential y-intercepts:
y + 12 = 0 --> y = -12
y - 10 = 0 --> y = 10
Therefore, the y-intercepts of the equation are y = -12 and y = 10.
So, the x-intercepts of the equation are x = 20 and x = -6, while the y-intercepts are y = -12 and y = 10.