Find the equation of the circle that has a diameter with endpoints located at (-3,6) and (9,6)
1 answer:
Answer:
The equation of the circle is:
Step-by-step explanation:
Notice that the points at the two extremes of the diameter they give you are both located along the line y=6, and are separated by each other the distance given by: 9-(-3) = 12. So the diameter of the circle is 12 units, and then its radius is half of that: 6 units. (r = 6).
Now the center of the circle must be located also on the line y=6, and its x position must be that of the equidistant point to the two extremes. that is: x center = 9-6 = 3
Then the center of the circle is at the point (3,6) in the plane.and its radius is r=6. With this info, we can use the standard equation for a circle of radius r and center :
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Answer:
The turning point of the graph is at (3,-16)
Step-by-step explanation:
The general equation of curve is given as:
y = x² + ax + b
The two point for which the equation satisfies is (0,-7) and (7,0).
Substitute (0,-7) in the general equation:
y = x² + ax + b
-7 = 0² + a(0) + b
b = -7
Substitute (7,0) in the general equation:
y = x² + ax + b
0 = 7² + 7a + b
Where b = -7
0 = 49 + 7a - 7
0 = 42 + 7a
a = -6
The equation of the curve is:
a = -6 and b = -7
y = x² + ax + b
y = x² - 6x - 7
Graph of the equation is attached below.
We can see that the the turning point of the graph is at (3,-16)
