Question

find the distance of the circle whose centre is at (2'0) and which passed though the point (7'_12)​

Answer 1

Question:-

find the diameter of the circle whose centre is at (2,0) and which passed though the point (7, -12)?

Solution:-

Let AB be the Diameter of the Circle

Let AB be the Diameter of the Circle& Co-ordinate of Circle ( O) = ( 2, 0).

Let the Co-ordinate of Point A be ( 7, -12) and that of B be ( x , y).

Given that C is the midpoint of AB.

Hence ,

Co - Ordinate of C = [ (x1+x2)/2, (y1+y2)/2]

:=) C = [ (x+7)/2,( y-12)/2]

A.T.Q.

:=) C = [ (x +7)/2=2. and. (y-12)/2=0]

:=) C = [ ( x + 7 = 4) and. ( y - 12 = 0) ]

:=) C = [ ( x = -3) and ( y = 12) ]

Hence the coordinates of B = (x,y) = ( -3,12).

So, The Co-ordinate of A and B are A(7,-12) B ( -3,12).

=) AB= √[ (x2 - x1)² + (y2-y1)²]

=) AB = √{ (-3 -7)²+[12-(-12)]²}

=) AB = √[ (-10)² + (24)²]

=) AB = √[ 100+ 576]

=) AB = √ 676

=) AB = √(26× 26)

=) AB = 26 units.

Hence,

Diameter of the Circle is 26 units.