Answer:
Step-by-step explanation:
Standard form of a circle is given by,
(x - a)² + (y - b)² = r²
Here, (a, b) is the center and 'r' is the radius of the circle.
For a circle having center (8, -4) and radius r = 1
Equation of the circle will be,
(x - 8)² + (y + 4)² = 1²
(x - 8)² + (y + 4)² = 1
Option (1) is the answer.
Question (2)
Circle with the center (-1, 0) and a point (2, -4) on it,
Radius of the circle = Distance between the center and the given point on circumference
= [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
= [tex]\sqrt{(-1-2)^2+(0+4)^2}[/tex]
= [tex]\sqrt{9+16}[/tex]
= 5
Therefore, equation of the circle will be,
(x + 1)² + (y - 0)² = 5²
(x + 1)² + y² = 25
