coordinate geometry: circles - The point P(–1, 1) and the point Q(7, –5) both lie on C center at (3, -2). (b) Show that PQ is a diameter of C.

Krishna (last edited 4 years ago) (Expert, Educator @Qalaxia)

Step 1: Calculate the midpoint of the points.

NOTE: Note down the endpoints (x_1, y_1) and (x_2, y_2) from the given points. And substitute the values into the midpoint formula.

[FORMULA: The midpoint formula is

M = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})

where M is the midpoint of a line segment with endpoints at [math] (x_1, y_1) \text{ and } (x_2, y_2).

Step 2: Compare the midpoint with the given center of the circle.

NOTE: If the midpoint of the two points and the center same then the distance between the two points shows the diameter of the circle.

Step 3: Calculate the distance between the two points.

NOTE: 2 * Radius = diameter

the Distance formula to find the equation of the circle.

d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2\ }\ -\ y_1\right)^2}\

EXAMPLE:Given points (2, 1)(10, 7)

r\ =\ \sqrt{\left(10\ -\ 2\right)^2\ +\ \left(7-2\right)^2}

r =\sqrt{64-36}v

r = 64−36

r =\sqrt{100}