Find the equation to the circle such that the points A(-3,5) and B(4,-2) form the ends of a diameter?
this is all the given information.
this is all the given information.
1 Answer
Explanation:
"the standard form of the equation of a circle is "
color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(2/2)|)))
"where "(a,b)" are the coordinates of the centre and r is"
"the radius"
"Given the endpoints of the diameter then the centre is "
"at the midpoint and the radius is the distance from the "
"centre to one of the endpoints"
"the coordinates of the midpoint are the average of the"
"the coordinates of the endpoints"
"midpoint "=[1/2(-3+4),1/2(5-2)]=(1/2,3/2)
"to calculate the radius use the "color(blue)"distance formula"
•color(white)(x)r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)
"let "(x_1,y_1)=(1/2,3/2)" and "(x_2,y_2)=(-3,5)
rArrr=sqrt((-3-1/2)^2+(5-3/2)^2
color(white)(r)=sqrt(49/4+49/4)=sqrt(98/4)
rArr(x-1/2)^2+(y-3/2)^2=(sqrt(98/4))^2
rArr(x-1/2)^2+(y-3/2)^2=49/2larrcolor(red)"equation of circle"
