Answer :
Answer:
Answer is C. 4x - 3y = 0
Step-by-step explanation:
To find the diameter of the circle x²+y²−6x−8y=0, we have to understand that one of the characteristic of diameter is that it passes through the center of the circle. Therefore, first we have to find the center of the circle, then check any of the equation passes through the center.
Equation of circle with center (a, b):
[tex]\boxed{(x-a)^2+(y-b)^2=r^2}[/tex]
[tex]x^2+y^2-6x-8y=0[/tex]
[tex](x^2-6x)+(y^2-8y)=0[/tex]
[tex][(x-3)^2-9]+[(y-4)^2-16]=0[/tex]
[tex](x-3)^2+(y-4)^2-25=0[/tex]
[tex](x-3)^2+(y-4)^2=5^2[/tex]
Hence the center = (3, 4)
To check if an equation passes through a point, we substitute the x and y with the point's coordinate and check if the equation is true.
Option A
[tex]y-3x=0[/tex]
[tex]4-3(3)=0[/tex]
[tex]-5=0[/tex]
The equation is false, so this is not the diameter.
Option B
[tex]3y-2x=0[/tex]
[tex]3(4)-2(3)=0[/tex]
[tex]6=0[/tex]
The equation is false, so this is not the diameter.
Option C
[tex]4x-3y=0[/tex]
[tex]4(3)-3(4)=0[/tex]
[tex]0=0[/tex]
The equation is true, so this is the diameter.
Option D
[tex]x+3y=0[/tex]
[tex]4+3(3)=0[/tex]
[tex]13=0[/tex]
The equation is false, so this is not the diameter.
