1. Given a circle with center (9, -2) and a point on the circle (10, -10). Note: You must support your answers algebraically.

Question

a. Is there a value y such that the point (-8, y) lies on this circle? Algebraically show there is no point or algebraically prove the point exists and find the point.

b. Is there a value x such that the point (x, -8) lies on this circle? Algebraically show there is no point or algebraically prove the point exists and find the point.

Answer 1

The distance from (9,-2) to (10,-10) = square root of 65 = radius of the circle.

The equation of the circle is $(x-9{)}^2+(y+2{)}^2=65$

Substituting -8 for x gives a quadratic which has solutions 70 and -73 for y, i.e. two points exist on the circle with ordinate -8.

The second question is solved in a similar way!