Help with a tig/algebra 2 trig homework question?

Question

a line segment through the center of the circle intersects the circle at the points (2,2) and (4,4) and the center of the circle is (3,3)...
what is the radius of the circle?
what is the equation of the circle in standard form?

Answer 1

Radius r = ?

Here radius r = Distance between the two points (2, 2) and (3, 3) or (3, 3) and (4, 4 )

Consider the points (2, 2) and (3, 3) and find the radius.

Formula : A(x₁, y₁) ,B(x₂, y₂) points distance: √[(x₂-x₁)² + (y₂-y₁)²]

Radius r = √ [(3-2)² + (3-2)²]

r = √ [(1)²+(1)²]     

r = √[1+1]   

r = √2

 

Standard form equation is (x – h)² + (y – k)² = r² where (h, k) is the Centre and r, the radius.

Here Centre (h, k) = (3, 3) and radius r = √2

(x – 3)² + (y – 3)²=(√2)² substitute Centre and radius in the formula

Note: (√A)² = A

(x – 3)² + (y – 3)² = (√2)²

Circle equation is

(x – 3)² + (y – 3)² = 2.