Question

What is the standard form of the equation of the circle in the graph?

Answer 1

Answer:

$(x-1)^2+(y-2)^2=16$

Step-by-step explanation:

The standard form of a circle is given by

$(x-h)^2+(y-k)^2=r^2$

Here, (h,k) is the center and r is the radius.

From the given graph,

center = (1,2)

thus, h = 1, k = 2

The distance from the center to any point on the circle is the radius.

Hence, radius is 4 units. r = 4

Substituting the values of h, k and r in the equation of circle

$(x-1)^2+(y-2)^2=4^2\\\\(x-1)^2+(y-2)^2=16$

Answer 2

Example 3: 2x2 + 2y2 = 8. (a) Find the center and radius of the circle. (b) Graph the circle.First divide the equation by 2. The new equation is :x2 + y2 = 4 .The standard form:(x - h)2 + (y - k)2 = r2(x - 0)2 + (y - 0)2 = (2)2. Now, you can identify the center correctly.