Question

A circle is centered at the origin and contains the point (-4, -3). What is the area of this circle?

Answer 1

The circle has center at teh origin ( 0,0) and a passing point ( -4, -3)

The general equation of circle is :

`\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{where, (a,b) are the center of the circle} \end{gathered}`

In the given question the center : ( 0,0)

So,

`\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}`

Since, the circle passes through ( -4, -3) so put x = -4 and y =-3 ans solve for r

`\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}`

Thus radius = 5

Equation of circle is :

`\begin{gathered} \mleft(x-0\mright)^2+\mleft(y-0\mright)^2=5^2^{} \\ x^2+y^2=25 \end{gathered}`

The general expression for the area pf circle is :

`\text{Area of circle = }\Pi(radius)^2`

Substitute the value of radius = 5

`\begin{gathered} \text{Area of circle = }\Pi(radius)^2 \\ \text{Area of circle = }\Pi5^2 \\ \text{Area of Circle = 25 }*3.14 \\ \text{Area of Circle = 78.5 unit}^(2) \end{gathered}`

So, Area of circle is 78.5 unit²

Answer : Area of circle is 78.5 unit²