What is the general form of the equation for the given circle? with coordinates (4,7) (7,4)
Answers
Answer:
Step-by-step explanation:
The equation of a circle is (x - xo)^2 + (y - yo)^2 = r^2, where (xo,yo) is the center of the circle and r is the radius of the circle.
From the figure you can calculate both the center (xo,yo) and the radius (r), using a fundamental assumption: that the two segments drawn form a 90° angle.
1) Center:
Note that the y-coordinate of the point B(7,4) is the same y-coordinate of the center of the circle, so yo = 4
And the x-coordinate of the point A(4,7) is the same x-coordinate of the center of the circle, so xo = 4
Then, the center is (4,4).
2) Radius, r
The radius may be calculated as the difference between the x-coordinates of the two points, i.e. 7 - 4 = 3.
Of course, it may also be calculated as the difference of the y-coordinates of the same two points, i.e.: 7 - 4 = 3.
Then, r = 3.
3) use the formula (x - xo)^2 + (y - yo)^2 = r^2
(x - 4)^2 + (y - 4)^2 = 3^2
And expand the parenthesis:
x^2 - 8x + 16 + y^2 - 8y + 16 = 9
x^2 - 8x + y^2 - 8y + 23 = 0
Answer:
We know Slope (m)=x2-x1/y2-y1
=7-4/4-7
=3/-3
=-1
Now, the format of equation is,
(y-y1)=m(x-x1)
=y-7=-1(x-4)
=y-7=-x+4
=x+y=4+7
=x+y=11