Respuesta :
The circle has center at teh origin ( 0,0) and a passing point ( -4, -3)
The general equation of circle is :
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{where, (a,b) are the center of the circle} \end{gathered}[/tex]In the given question the center : ( 0,0)
So,
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ (x-0)^2+(y-0)^2=r^2 \\ x^2+y^2=r^2 \end{gathered}[/tex]Since, the circle passes through ( -4, -3) so put x = -4 and y =-3 ans solve for r
[tex]\begin{gathered} x^2+y^2=r^2 \\ (-4)^2+(-3)^2=r^2 \\ 16+9=r^2 \\ r^2=25 \\ r=\sqrt[]{25} \\ r=5 \end{gathered}[/tex]Thus radius = 5
Equation of circle is :
[tex]\begin{gathered} \mleft(x-0\mright)^2+\mleft(y-0\mright)^2=5^2^{} \\ x^2+y^2=25 \end{gathered}[/tex]The general expression for the area pf circle is :
[tex]\text{Area of circle = }\Pi(radius)^2[/tex]Substitute the value of radius = 5
[tex]\begin{gathered} \text{Area of circle = }\Pi(radius)^2 \\ \text{Area of circle = }\Pi5^2 \\ \text{Area of Circle = 25 }\times3.14 \\ \text{Area of Circle = 78.5 unit}^{2} \end{gathered}[/tex]So, Area of circle is 78.5 unit²
Answer : Area of circle is 78.5 unit²
