How do you find an equation of the circle that satisfies the given conditions: endpoints of a diameter are P(−1, 2) and Q(7, 8)?

2 Answers
Apr 16, 2018

Answer:

#color(blue)((x-3)^2+(y-5)^2=25)#

Explanation:

The coordinates of the centre of the circle will be the coordinates of the midpoint of the diameter.

#((-1+7)/2,(2+8)/2)=(3,5)#

We next find the length of the diameter using the distance formula:

#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#d=sqrt((7-(-1))^2+(8-2)^2)=sqrt(100)=10#

This is the length of the diameter, so radius is:

#r=10/2=5#

The equation of a circle is given as:

#(x-h)^2+(y-k)^2=r^2#

Where #h and k# are the #x and y# coordinates of the centre respectively.

#:.#

#(x-3)^2+(y-5)^2=25#

Apr 16, 2018

Answer:

#( x-3)^2 + (y-5)^2 = 25#

Explanation:

Equation of a circle is of the form: #(x-a)^2 + (y-b)^2 = r^2#
Where (a,b) represents the co ordinates of the circle's centre
And 'r', the circle's radius
Equation to find the coordinates of the centre of a line segment is
= #((x1 + x2)/2) , ((y1 + y2)/2)#
Hence,
( 0.5 ( -1 + 7 ) ) , ( 0.5 ( 2 + 8 ) )
= ( 3 , 5 )
For the distance between two points , #sqrt(( x2 - x1 )^2 + ( y2 - y1 )^2)#
Hence, #sqrt( ( 7 - ( -1 ) )^2 + ( 8 - 2 )^2#
= 10
Diameter of circle = 10
Radius , r = 5
= #( x - 3 )^2 + ( y - 5 )^2 = 5^2#
= #( x - 3 )^2 + ( y- 5 )^2 = 25 #