A circle passes through the points (2,3) and (4 , 5). If its centre lies on the line, y-4 x+3=0 , then its radius is equal to

Step-by-step solution

Equation of the line passing through the points (2,3) and (4,5) is y-3= ( 5-3 4-2 ) x-2 x-y+1=0 Equation of the perpendicular line passing through the midpoint (3,4) is x+y-7=0 Lines (1) and (2) intersect at the center of the circle. So, the center of the circle is (3,4) Therefore, the radius is aligned & (x₂-x₁ )^2+ (y₂-y₁ )^2 &= (2-3)^2+(3-4)^2 = 2 units. aligned