Answer: Yes, (4, - 4) lies on this circle.
Step-by-step explanation:
Equation of circle:[tex](x-h)^2+(y-k)^2=r^2[/tex] , where (h,k) = center , r = radius
Given: A circle has a center located at (-2, 4) and a radius of length 10.
i.e. (h,k) =(-2,4) and r= 10
Equation of circle will be:
[tex](x-(-2))^2+(y-4)^2=10^2\\\\\Rightarrow\ (x+2)^2+(y-4)^2=100[/tex] (i)
If (4, - 4) lies on this circle , then it must satisfy the above equation.
To check put x= 4 , y=-4 in (i)
[tex](4+2)^2+(-4-4)^2=100\\\\\Rightarrow\ 6^2+(-8)^2=100\\\\\Rightarrow\ 36+64=100\\\\\Rightarrow\ 100=100[/tex] which is true.
Hence, (4, - 4) lies on this circle.
Equation of the circle is the way to represent the circle with the the center point and radius length in the coordinate plane. As the point (4,-4) satisfy the equation of the circle. Hence the point (4,-4) lies on the given circle.
Given information-
A circle has a center located at (-2, 4).
The radius of the circle is 10 units.
Equation of the circle is the way to represent the circle with the the center point and radius length in the coordinate plane.
The standard equation of the line is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here h and k are the center point.
Keep the value,
[tex]\begin{aligned}(x-(-2))^2+(y-4)^2&=10^2\\ (x+2)^2+(y-4)^2&=100\\ \end[/tex]
If the given points (4,-4) lies on the circle then these points must satisfy the equation of the circle. Thus,
[tex]\begin{aligned} (x+2)^2+(y-4)^2&=100\\ (4+2)^2+(-4-4)^2&=100\\ 6^2+(-8)^2&=100\\ 36+64&=100\\ 100&=100\\ \end[/tex]
As the point (4,-4) satisfy the equation of the circle. Hence the point (4,-4) lies on the given circle.
Learn more about the equation of the circle here;
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