Question

Write the equations of these circles.

a) Centre origin, radius 3/2
b) Centre origin, radius 0.5
c) Centre origin, radius root 3​

Answer 1

The standard form equation of a circle centered at the origin is (x - h)² + (y - k)² = r². For circles with a center at the origin, the equations are x² + y² = (3/2)², x² + y² = (0.5)², and x² + y² = (√3)², corresponding to radii of 3/2, 0.5, and √3 respectively.

Step-by-step explanation:

The equations for circles with the center at the origin (0,0) in a coordinate system can be written using the standard form equation of a circle which is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle and r is the radius.

• For a circle with a center at the origin and radius 3/2, the equation is x² + y² = (3/2)².
• For a circle with a center at the origin and radius 0.5, the equation is x² + y² = (0.5)².
• For a circle with a center at the origin and radius √3, the equation is x² + y² = (√3)².

Answer 2

I attached an image cause it’s easier to explain the answers. I just want to add that if the centre of a circle is the origin it means that it has the coordinates (0,0).
Hope this helps