Answer:

Step-by-step explanation:
Given:
Center of circle is at (5, -4).
A point on the circle is 
Equation of a circle with center
and radius 'r' is given as:

Here, 
Radius of a circle is equal to the distance of point on the circle from the center of the circle and is given using the distance formula for square of the distance as:
Using distance formula for the points (5, -4) and (-3, 2), we get

Therefore, the equation of the circle is:

Now, rewriting it in the form asked in the question, we get

Answer:
x = 1, y = 10
Step-by-step explanation:
y = -5x + 15 --- Equation 1
2x + y = 12 --- Equation 2
Substitute y = -5x + 15 into Equation 2:
2x + y = 12
2x - 5x + 15 = 12
Evaluate like terms.
15 - 3x = 12
Isolate -3x.
-3x = 12 - 15
Evaluate like terms.
-3x = -3
Find x.
x = -3 ÷ -3
x = 1
Substitute x = 1 into Equation 2:
2x + y = 12
2(1) + y = 12
2 + y = 12
Isolate y.
y = 12 - 2
y = 10
Given that,
Point 1 = (-6,9)
Point 2 = (2,9)
To find,
The slope of a line that passes through the given pair.
Solution,
We have,
x₁ = -6, x₂ = 2, y₁ = 9, y₂ = 9.
The formula for the slope of a line is given by :

Hence, the slope of the line that passes through the given pair is 0.
Answer:
1423/33
Step-by-step explanation:
Let x = 43.121212.........
Two digits are repeating after decimal point. So multiply both sides by 100
100x = 4312.1212 --------------(I)
<u> x = 43.1212 </u> -----------(II) { subtract equation (II) form (I)}
99x = 4269
x= 4269/99 {reduce to simplest form by giving by 3rd table}
x = 1423/33