1 / 9
00
The Pythagorean theorem relates the sides of a right triangle. How is it used to derive the equation of a circle?
By finding the hypotenuse of a triangle inscribed in the circle
By expressing the distance between a point on the circle and the center using the theorem
By calculating the angles formed by the diameter of the circle
What is the geometric definition of the center of a circle?
The midpoint of any two points on the circle
The point of intersection of two diameters
The point equidistant from all points on the circle
Equation of circle with center (-2,0,3) and radius 1 is
(x+2)2+y2+(z−3)2=1\left(x+2\right)^2+y^2+\left(z-3\right)^2=1(x+2)2+y2+(z−3)2=1
(x+2)2+(z−3)2=1\left(x+2\right)^2+\left(z-3\right)^2=1(x+2)2+(z−3)2=1
none
Fill in the blanks:
The center of circle(x+5)2+(y+1)2+(z−3)2=49\left(x+5\right)^2+\left(y+1\right)^2+\left(z-3\right)^2=49(x+5)2+(y+1)2+(z−3)2=49 is
(-5,-1,3)
(-5,1,3)
(-5,-1,-3)
The radius of circle(x−7)2+(y−3)2=121\left(x-7\right)^2+\left(y-3\right)^2=121(x−7)2+(y−3)2=121 is
11
15
121
The center of circle (x−7)2−(y−3)2=121\left(x-7\right)^2-\left(y-3\right)^2=121(x−7)2−(y−3)2=121 is
(7,3)
(7,-3)
(-7,3)
Which of the following statements is true regarding the radius of a circle?
The radius is half the diameter of the circle.
The radius is always larger than the diameter.
The radius is the length of a chord within the circle.
Equation of circle with center origin and radius 5 is _______.
x2+y2=25x^2+y^2=25x2+y2=25
x2−z2=25x^2-z^2=25x2−z2=25
x2−y2+z2=25x^2-y^2+z^2=25x2−y2+z2=25
Equation of circle with center (1,1) and radius 3 is
(x−1)2+(y−1)2=9\left(x-1\right)^2+\left(y-1\right)^2=9(x−1)2+(y−1)2=9
(x−1)2−(y−1)2=9\left(x-1\right)^2-\left(y-1\right)^2=9(x−1)2−(y−1)2=9
It is done.