Question

Graph the line and the circle (x-1)²+(y-2)²=2² and y=2x+2.

Answer 1

Answer:

The graph of the line and the circle is in the attachment.

Step-by-step explanation:

In order to graph the circle, you have to use the circle equation formula to obtain the center and the radius.

(x-xo)² + (y-yo)² = r²

where the point (xo,yo) is the center and r is the radius.

Using the given formula, the center is:

xo=1, yo=2

(1,2)

And the radius is:

r=2

Now you have to graph the point (1,2) and draw a circle centered at that point, with a distance of 2 from the center.

To obtain the exact values of the intersection of the circle with the x-axis you have to replace y=0 in the equation and solve it for x. For the points of intersection with the y-axis you have to replace x=0 in the equation and solve it for y.

-For x=0, solving for y:

(0-1)²+(y-2)²=2²

1+(y-2)²=4

(y-2)²= 3

Applying the squareroot both sides

y-2 = ± √3

y1= -√3 +2

y2= √3 +2

P1(0, -√3 +2) and P2(0, √3 +2)

-For y=0

(x-1)²+(0-2)²=2²

(x-1)² + 4 = 4

(x-1)² = 0

Applying the squareroot both sides:

x-1 = √0

x-1=0

x=1

P3 (1,0)

In order to graph the linear equation, you have to obtain the intersection with the x-axis replacing y=0 in the equation and the intersection with the y-axis replacing x=0 in the equation. That way, you obtain two point of the line and then you have to trace the line containing those points.

-For x=0

y=2(0)+2 =2

P1 (0,2)

-For y=0

0= 2x+2

Adding -2 both sides

2x= -2

Dividing by 2 both sides

x= -1

P2(-1,0)