Question

the equation of the circle with AB as a diameter, whose coordinates are A(2,5),B(8,13)

Answer 1

Answer:

slope (m)=(y2-y1)/(x2-x1)

=(13-5)/(8-2)

=8/6

=4/3

now,the equation is,

y-y1=m(x_x1)

=y-5=4/3(x-2)

=3y-15=4x-6

=4x-3y+9=0....... answer.

i hope it had helped u.........

byeeeee

Answer 2

Step-by-step explanation:

the coordinates of diameter are,

A (2,5) = (x1, y1)

B (8,13) = (x2 , y2)

let us consider the centre of the circle is p, coordinates of p ( h,k)

find the coordinates of the centre by midpoint formula,

p(h, k) = ((x1+ x2)/2 ) ,(( y1 + y2)/2)

= ( (2 + 8 )/2 ) , ( 5 + 13) / 2 )

= (( ( 10 ) /2 ) , ( (18) / 2))

= (5 , 9 )

Now find the length of diameter by distance formula,

Distance = √[(y2 - y1)² + (x2 - x1)²]

= √[ (13 -5)² + ( 8 - 2)²]

= √ [ ( 8)² + ( 6)² ]

= √ [ 64 + 36 ]

= √ ( 100)

= 10

radius = 1/2 ( diameter)

= 1 /2 ( 10 )

= 5

Now, find the equation of circle by centre radius form

centre radius form :

r² = ( x - h) ² + ( y - k) ²

we have, ( h , k ) = (5 , 9 ) And r = 5

(5)² = ( x - 5 )² + ( y - 9)²

25 = (x²+25-10x)+(y²+81-18y)

25 = x² + y² -10x - 18y + 25 + 81

25 - 106 = x² + y² -10x - 18y

-81 = x² + y² -10x - 18y

x² + y² -10x - 18y + 81 = 0

x² + y² -10x - 18y + 81 = 0 is the final equation of a given circle