Question

find the equation of circle with (2,3) and (6,9) as end points of diameter.
And also find the RADIUS , CENTRE of the Circle.

Answer 1

Answer:

Centre:  (4, 6)

Radius:  √13

Equation:  ( x - 4 )² + ( y - 6 )² = 13

Step-by-step explanation:

The centre is at the midpoint of the diameter, so:

centre = ( (2+6)/2, (3+9)/2 ) = (4, 6)

The radius is the distance from the centre to any point on the circle.  So it is the distance from (2, 3) to (4, 6):

r = √( (4-2)² + (6-3)² ) = √( 2² + 3² ) = √(4+9) = √13

The equation has the form

( x - a )² + ( y - b )² = r²

where (a, b) is the centre.  So a = 4, b = 6, r = √13 and the equation is:

( x - 4 )² + ( y - 6 )² = 13