Question

The points (7,3), (2,8) and (-3,3) lie on a circle.Find the equation

Answer 1

Answer:

Step-by-step explanation:

Let L1 and L2 be the perpendicular bisectors of PQ and QR respectively.

Mid-point of PQ

Mid-point of QR

Gradient of PQ

Gradient of QR

Since L1 ^ PQ, L2 ^ QR,

Gradient of L1

Gradient of L2 =

L1 :

L2 :

Find the mid-points of two chords.

Find the gradient of two chords.

Product of gradients of perpendicular lines = -1

Find the equations of perpendicular bisectors using gradient-point form.

(1) – (2),

\ x = 1 …. (3)

Subst. (3) in (1), \ y = 3

\ C = (1,3)

Solve for the center.

r = |PC|

Solve for the radius.

The equation of the circle is