SOLUTION: Graph the circle with center at (-1, -2), which also passes through the point (0, 2). Label the center and at least four points on the circle. Write the equation of the circle

Algebra ->  Circles -> SOLUTION: Graph the circle with center at (-1, -2), which also passes through the point (0, 2). Label the center and at least four points on the circle. Write the equation of the circle      Log On


   

Question 947528: Graph the circle with center at (-1, -2), which also passes through the point (0, 2). Label the center and at least four points on the circle. Write the equation of the circle
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
r for radius

r=sqrt%28%28-1-0%29%5E2%2B%28-2-2%29%5E2%29
sqrt%28%281%29%5E2%2B%280%29%5E2%29
sqrt%281%29
r=1

EQUATION: highlight%28%28x%2B1%29%5E2%2B%28y%2B2%29%5E2=1%29

The small blue curve mark is the location for the center point of the circle.

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Graph the circle with center at (-1, -2), which also passes through the point (0, 2). Label the center and at least four points on the circle. Write the equation of the circle
Equation of a circle: sqrt%28%28x+-+h%29%5E2+%2B+%28y+-+k%29%5E2%29+=+r

With the point, (0, 2), and center coordinates, or (h, k) being: (- 1, - 2), we get: 

sqrt%28%280+-+-+1%29%5E2+%2B+%282+-+-+2%29%5E2%29+=+r

sqrt%28%280+%2B+1%29%5E2+%2B+%282+%2B+2%29%5E2%29+=+r

sqrt%281+%2B+16%29+=+r

sqrt%2817%29+=+r

Thus, the equation becomes: highlight_green%28sqrt%28%28x+%2B+1%29%5E2+%2B+%28y+%2B+2%29%5E2%29+=+sqrt%2817%29%29. Squaring both sides results in: %28x+%2B+1%29%5E2+%2B+%28y+%2B+2%29%5E2+=+17

When plotting this graph, you'll notice that its center is at: (- 1, - 2), it has a radius of: sqrt%2817%29,

and one of its points is: (0, 2). This point is on its circumference, and will also be on the y-axis. 

Since y is 0 on the x-axis, substituting 0 for y will give you 2 more coordinate points: the x-intercepts. 

The 4th and final point is obtained by substituting 0 for x in the equation. This will give you the point (0, 2),

and another in the form of (0, y). 

You now have 4 points.