Asked by Karina Herrera on Apr 23, 2024
Verified
Identify the center and radius of the circle 4x2+4y2=14 x ^ { 2 } + 4 y ^ { 2 } = 14x2+4y2=1 .
A) center: (0,0) radius: 14\frac { 1 } { 4 }41
B) center: (1,1) radius: 4
C) center: (1,1) radius: 2
D) center: (2,2) radius: 1
E) center: (0,0) radius: 12\frac { 1 } { 2 }21
Center
The middle point of a shape, object, or group of points, often equidistant from all outer edges or surfaces.
Radius
The distance from the center to the circumference of a circle or sphere.
- Acquire expertise in composing and identifying the conventional representations of circle equations.
- Build the capacity to spot significant features of conic sections, such as the center, radius, vertices, co-vertices, and foci.
Verified Answer
LM
luqman majid4 days ago
Final Answer :
E
Explanation :
We can rewrite the given equation as $x^2 + y^2 = \frac{1}{4}$, which is in standard form of a circle centered at the origin with radius $\frac{1}{2}$. Therefore, the center is $(0,0)$ and the radius is $\frac{1}{2}$. Thus, the best choice is E.
Learning Objectives
- Acquire expertise in composing and identifying the conventional representations of circle equations.
- Build the capacity to spot significant features of conic sections, such as the center, radius, vertices, co-vertices, and foci.