Question

if a circle of radius 5 was centred on the point C(3,8), if two points on the edge are A(6,4) and B(-1,11): prove that both A and B are points on the edge of the circle

Answer 1

Answer on Question #62887 – Math – Analytic Geometry

Question

If a circle of radius 5 was centred on the point C(3,8), if two points on the edge are A(6,4) and B(-1,11): prove that both A and B are points on the edge of the circle.

Solution

The equation of this circle is

$$(x - 3)^2 + (y - 8)^2 = 25.$$

If A and B are both points on the edge, then their coordinates will satisfy the equation of circle. Substituting the coordinates of A we shall have

$$\begin{array}{l} (6 - 3)^2 + (4 - 8)^2 = 9 + 16 = 25; \\ 25 = 25, \end{array}$$

which is true.

Therefore, A is indeed a point on the edge of circle.

Substituting the coordinates of A we shall have

$$\begin{array}{l} (-1 - 3)^2 + (11 - 8)^2 = 16 + 9 = 25; \\ 25 = 25, \end{array}$$

which is true.

Therefore, B is indeed a point on the edge of circle.

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