Answer:
The correct answer is option (b).
Therefore the area of the circle is [tex]=20 \pi[/tex] square units
Step-by-step explanation:
Given that , P(3,2) and Q(7,10) are the endpoint of the diameter of a circle.
To find out the length of diameter we use the distance formula.
If (x₁,y₁) and (x₂,y₂) are point.
Then the distance between them is = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Here x₁=3,y₁=2,x₂ = 7,y₂=10.
The length of the diameter is = [tex]\sqrt{(7-3)^2+(10-2)^2}[/tex]
[tex]=\sqrt{80}[/tex] units.
Radius of a circle [tex]=\frac{Dameter}{2}[/tex]
Therefore the the radius of the circle is [tex]=\frac{\sqrt{80}}{2}[/tex] units [tex]=\frac{2\sqrt{20} }{2}[/tex] units [tex]=\sqrt{20}[/tex] units
The area of a circle = [tex]\pi r^2[/tex]
Therefore the area of the circle is [tex]=\pi (\sqrt{20})^2[/tex]
[tex]=20 \pi[/tex] square units
