27. The center of a circle has coordinates.......

Question

27. The centre of a circle has coordinates (0,0) One end of a diameter is located at (7,-2)

a) What are the coordinates of the other endpoint of this diameter? 

b) What is the equation of the circle? 

Answer 1

a)

(0, 0) is the midpoint of the diameter. Use the midpoint formula to determine the other end point.

Use Pythagoras to determine the length of the radius.

b)

x² + y² = r², r being the radius you determined in a).

Answer 2

Imagine 'walking' out from the origin to one endpoint at (7,-2).  Now go back & imagine walking out from the origin in the opposite direction to the other endpoint...that would be at (-7,2), wouldn't it?  That answers (a).

 

you can figure the radius by using Pythagorean Theorem. The circle's equation is x² + y² = r²