Answer:
- x² +y² -6x -4y -3 = 0
- x² +y² -10x +4y = 0
see the attachment for graphs of these
Explanation:
You want the general form equation and graph of circles with the given center and (1) radius 4, and (2) through point (0, 0).
Equation of a circle
The standard-form equation of a circle with radius r and center (h, k) is ...
(x -h)² +(y -k)² = r²
The general form equation will be a rearrangement of this:
x² +y² -2hx -2ky +(h² +k² -r²) = 0
1.
The center is (h, k) = (3, 2), and the radius is r = 4. Put these values in the above equation:
(x -3)² +(y -2²) = 4² . . . . standard form
x² +y² -6x -4y -3 = 0 . . . . general form
2.
For this one, you don't know the radius, but you know a point that satisfies the equation. Using the point coordinates for x and y, you can find the necessary radius (squared).
The center is (h, k) = (5, -2), and point (x, y) = (0, 0) satisfies the equation.
(x -5)² +(y -(-2))² = (0 -5)² +(0 -(-2))² = 25 +4
(x -5)² +(y +2)² = 29 . . . . standard form
x² +y² -10x +4y = 0 . . . . general form