Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
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.
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.
