The points (0,6), (9,0), (0,-6) and (-k,0) lie on the circumference of a circle. Find the value of k.
Coordinate Geometry questions should also be started by sketching the information. That is if a diagram is not provided.
By symmetry, the centre of this circle will lie on the x-axis. As a result, b=0 in the formula for a circle, i.e. becomes . See more on the equation of a circle.
Substituting (0,6), (9,0) and (0,-6) into the equation of the circle gives and . Note that (0,-6) doesn’t give any more information than (0,6) does (this is because we used this information when deciding the centre lies on the x-axis). Combining the two gives . Solving this for a gives a=5/2. It follows that . Hence, the equation of the circle becomes Substituting (-k,0) into this equation gives . Solving this for k gives k=4, as required.