If a circle has a diameter with endpoints of (-3, 0) and (5, 4) then the equation of the circle is?

(x - 1)² + (y - 2)² = 20

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given the endpoints, then the centre is at the midpoint

C = [ , ] = (1, 2 )

The radius is the distance from the centre to either of the 2 endpoints.

Use the distance formula to find r

r =

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ )= (- 3, 0)

r =

  =

  =

  =

Thus equation of circle is

(x - 1)² + (y - 2)² = ( )² , that is

(x - 1)² + (y - 2)² = 20

27/4x^6 y^8

step-by-step explanation:

4(3x^2y^4)^3 (2x^3y^5)^4

=

108x^6 y^12 /16x^12 y^20

=

108 /16x^6 y^8

=

27 /4x^6 y^8