Maths, Co ordinate geometry

Question

A circle has diameter AB, where

A = (2, −5) and B = (−4, 7).
(a) Find the centre C and radius r of the circle.
(b) Use the distance formula to test whether P(6, −1) lies on the circle

 

 

Just struggling with these questions

Answer 1

The center must be the midpoint of AB.

Find coordinates of center, therefore, by using the midpoint formulas (in short, x,y)= (average x, average y).  

Then you can find equation of that circle, easily, and see if (6,-1) satisfies it.

Or, as the part b directs, you can calculate distance from center to P and see if that equals the radius, radius being the distance from center to either A or B.

 

Time formulas!

Answer 2

xm=(x1+x2)/2 ₌ (2-4)/2 = -2/2 = -1

ym=(y₁+y₂)/2 = (-5+7)/2 = 2/2 - 1

C(-1,1)

AB = √[(x₂-x₁)² + (y₂-y₁)²] = √[(-4-2)² + (7+5)²]

AB = √(36+144) = √180 = 6√5

radius = 1/2 AB = 3√5

d = √[(6+1)² + ( -1-1)²] = √[7² + (-2)²]

d = √(49+4) = √53

√53 ≠ 3√5 so P(6,-1) does not lie on the circle.