Question

Write the standard form of the equation of the specified circle. Endpoints of a diameter: (−x, −y), (x, y)

Answer 1

SOLUTION IS

WE KNOW STANDARD EQUATION OF CIRCLE
`[tex](X-a)^(2)`+
`(Y-b)^(2)`=
`r^(2)`

where (a,b) is centre and r is radius of circle

now we have to find component of centre and radius

we know centre of circle is equidistance from end points of diameter

apply formula to find mid point of line( (x1+x2)/2,(y1+y2)/2) we get

((x-x)/2,(y-y)/2)=(0,0)

hence component of circle is (0,0)

now apply distance formula between (0,0)and (x,y)

we get
`x^(2)`+
`y^(2)`=
`r^(2)`

hence standard equation of circlre is =
`X^(2)`+
`Y^(2)`=
`x^(2)`+
`y^(2)`