Find the equation of the circle with radius 1 and center C(1, -2). Then sketch its graph.
AND...
Sketch a graph of the circle given by the equation.
(x + 6)2 + (y – 4)2 = 16
For any centre (a,b) and radius r, the equation of the circle is
(x-a)^2 + (y-b)^2 = r^2
look at your second equation,
(x+6)^2 + (y-4)^2 = 16 or 4^2
doesn't it fit that pattern perfectly ?
for a centre of (-6,4) and radius of 4
Now you can sketch it.
Do the same for the first of your questions.
To find the equation of a circle with radius 1 and center C(1, -2), we can use the standard form equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius.
In this case, the center of the circle is C(1, -2), so h = 1 and k = -2. The radius is given as 1, so r = 1. Plugging these values into the standard form equation, we get:
(x - 1)^2 + (y + 2)^2 = 1^2
(x - 1)^2 + (y + 2)^2 = 1
Now let's sketch its graph. To do this, we need to plot the center of the circle, which is C(1, -2), and then use the radius of 1 to plot points on the circumference of the circle.
Using the center (1, -2) as a starting point, move 1 unit to the right (x + 1), and 1 unit up (y + 1), we can plot a point on the circumference of the circle. Repeat this process for all four directions (left, right, up, and down) to get a good approximation of the circle.
Now, let's move on to the next question.
To sketch the graph of the circle given by the equation (x + 6)^2 + (y - 4)^2 = 16, we can first identify the center and the radius of the circle.
Comparing the given equation to the standard form equation (x - h)^2 + (y - k)^2 = r^2, we can see that the center of the circle is (-6, 4) (opposite sign of the terms) and the radius is the square root of 16, which is 4.
Now, starting from the center (-6, 4), we can plot this point on the graph. Then, using the radius of 4, we can go 4 units in each direction (left, right, up, and down) from the center and plot points on the circumference of the circle.
By connecting these plotted points, we can obtain a smooth curve that represents the graph of the circle.