Answer :
Answer:
The answer to your question is (x - 5)² + (x + 4) = 100
Step-by-step explanation:
Data
Center = (5, -4)
Point = (-3, 2)
Process
1.- Calculate the length of the radius
Formula
d = [tex]\sqrt{(x2-x1)^{2} + (y2 - y1)^{2}}[/tex]
Substitution
d = [tex]\sqrt{(-3-5)^{2}+ (2 + 4)^{2}}[/tex]
Simplification
d = [tex]\sqrt{(-8)^{2}+ (6)^{2}}[/tex]
d= [tex]\sqrt{64 + 36}[/tex]
d = [tex]\sqrt{100}[/tex]
d = 10
2.- Get the equation of the line
h = 5 k = -4 r = 10
( x - 5)² + (y + 4)² = 10²
Simplification and result
(x - 5)² + (x + 4) = 100
Answer:
The first space is 3,
The second space is -2
The third space is 100
Step-by-step explanation:
A circle with center (a, b) and has radius r has equation: [tex](x-a)^{2} + (y-b)^{2} = r^{2}[/tex]
Now, if the circle passes through (-3, 2) and it has center on (5, -4). That means the radius of the circle will be the distance between points (-3, 2) and (5, -4).
[tex]d = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }[/tex]
where d = formula of distance between points [tex](x_{2}, y_{2} ) \ and \ (x_{1}, y_{1} )[/tex]
[tex]d = \sqrt{(-3-5)^{2} + (-4-2)^{2} }\\ d = \sqrt{-8^{2} + -6^{2} }\\ d = \sqrt{64+36}\\ d = \sqrt{100}\\ d = radius \ of \ circle = 10[/tex]
Now, with r = 10, a = -3, b = 2
The equation of circle becomes:
[tex](x-(-3))^{2} + (y-2)^{2} = 10^{2} \\(x+3)^{2} + (y-2)^{2} = 100 \\[/tex]
The first space is 3,
The second space is -2
The third space is 100