9514 1404 393
Answer:
(x +3)² +(y -4)² = 145
Step-by-step explanation:
The center of the circle is the midpoint of the given segment PQ. If we call that point A, then ...
A = (P +Q)/2
A = ((-12, -4) +(6, 12))/2 = (-12+6, -4+12)/2 = (-6, 8)/2
A = (-3, 4)
The equation of the circle for some radius r is ...
(x -(-3))² +(y -4)² = r² . . . . . . where (-3, 4) is the center of the circle
The value of r² can be found by substituting either of the points on the circle. If we use Q, then we have ...
(6 +3)² +(12 -4)² = r² = 9² +8²
r² = 81 +64 = 145
Then the equation of the circle is ...
(x +3)² +(y -4)² = 145
Answer:
y = 3x - 5
Step-by-step explanation:
We know that the equation 'y = 3x + ?' intersects the point (1, -2). This means that when x = 1, y = -2 in out equation above. To solve this just plug in the x and y values to get '?'.
Now that we know '?' is -5, we write it back into slope intercept form, so our final answer is y = 3x - 5