Respuesta :
Answer: The required equation of the circle is [tex]x^2+y^2+6.4x+4.2y=3.84.[/tex]
Step-by-step explanation: We are given to find the equation of the circle with center (3.2,-2.1) and radius 4.3.
We know that
the STANDARD equation of a circle with center (h, k) and radius r units is given by
[tex](x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
For the given circle,
center, (h, k) = (3.2, -2.1) and radius, r = 4.3 units.
So, from equation (i), we get
[tex](x-3.2)^2+(y-(-2.1))^2=(4.3)^2\\\\\Rightarrow (x-3.2)^2+(y+2.1)^2=18.49\\\\\Rightarrow x^2-6.4x+10.24+y^2+4.2y+4.41=18.49\\\\\Rightarrow x^2+y^2-6.4x+4.2y+14.65=18.49\\\\\Rightarrow x^2+y^2+6.4x+4.2y=18.49-14.65\\\\\Rightarrow x^2+y^2+6.4x+4.2y=3.84.[/tex]
Thus, the required equation of the circle is [tex]x^2+y^2+6.4x+4.2y=3.84.[/tex]
