Pregunta
Find the center and radius of the circle having the given equation.
Ask by Turner Dickson. in the United States
Jan 31,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The center of the circle is at
and the radius is
.
Solución
The given equation of the circle is:
This equation is in the standard form of a circle:
where
is the center of the circle and
is the radius.
Comparing the given equation with the standard form:
- There are no
or linear terms, which implies that and . - The right-hand side of the equation is
, which is equal to . Therefore, .
Final Answer:
- Center:
- Radius:
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Mind Expander
The given equation of the circle is
. To find the center and radius, we can compare this with the standard form of a circle’s equation, which is
, where
is the center and
is the radius.
In this case, since there are no
and
values shifting the circle away from the origin, the center is at
. The radius can be found by taking the square root of 64, which gives us
. So, the center of the circle is at
and the radius is
.
For a quick recap:
Center:
Radius:
Center:
Radius:
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