Respuesta :
Answer:
D
Step-by-step explanation:
The equation of the circle is (x-x0)^2 + (y-y0)^2 = r^2, where (x0,y0) is the center of the circle. Radius is the distance from any point to the center. Using distance formula you get r = 3.
The equation of the circle having center at point (4,1) and passing through the point (4,-2) is Option (D) [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]
Equation of circle in parametric form -
A circle having radius r and having center at (x0,y0) can be represented by the parametric equation as -
[tex](x - x0)^{2} + (y - y0)^{2} = r^{2}[/tex]
Any point say (x1,y1) which lies on the circle, must satisfy the given parametric equation of the circle.
How to frame the equation of circle from the information given in the question ?
Given that the point (4,-2) lies on the circle. Also the center of circle is at (4,1). Therefore, calculating the radius of the circle which is the distance from the center to the point lying on the circle.
Using distance formula,
radius = [tex]\sqrt{(4 - 4)^{2} + (-2 - 1)^{2} }[/tex] = [tex]\sqrt{9 }[/tex] = [tex]3[/tex]
Thus forming the equation of circle from the general parametric equation,
⇒ [tex](x - 4)^{2} + (y - 1)^{2} = 3^{2}[/tex]
∴ [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]
Therefore the equation of circle is Option (D) [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]
To learn more about equation of circle, refer -
https://brainly.com/question/10368742
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