Question

find equation of the circle with center (5/2,-4/3) and radius 6​

Answer 1

Answer:

x^2 + y^2 - 5x + 8y/3 = 26.862

Step-by-step explanation:

the general equation of the circle is (x-h)^2+(y-k)^2=r^2

here h is 5/2

k is -4/3

and r is radius that is 6

∴ (x-5/2)^2 + (y+4/3)^2 = 36

x^2 + 25/4 - 5x + y^2 + 16/9 + 8y/3 = 36

x^2 + y^2 - 5x + 8y/3 = 26.862

hope it is helpful......................

Answer 2

General equation of circle : (x - a)² + (y - b)² = R²

Here, a and b are the co-ordinates of centre and R is the radius.

Given : a = $\sf{{\dfrac{5}{2}}}$ , b = $\sf{{\dfrac{- 4}{3}}}$

            R = 6

⇒ $\sf{ \left[ x - \left( {\dfrac{5}{2}} \right) \right]^2 + \left[ x - \left( {\dfrac{- 4}{3}} \right) \right]^2 = 6^2 }$

⇒ ${\boxed{\sf{ \left( x - {\dfrac{5}{2}} \right)^2 + \left( x + {\dfrac{4}{3}} \right)^2 = 6^2 }}}$