Lines x and y are parallel. Write an equation that represents the relationship between b and e. Explain how you know this equati
on is always true
1 answer:
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Answer:
(x - 8)² + (y + 6)² = 25
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
Here (h, k ) = (8, - 6 ) , then
(x - 8)² + (y - (- 6))² = r² , that is
(x - 8)² + (y + 6)² = r²
The radius is the distance from the centre to a point on the circle
Calculate r using the distance formula
r =
with (x₁, y₁ ) = (8, - 6 ) and (x₂, y₂ ) = (5, - 2 )
r =
=
=
=
=
= 5
Then equation of circle is
(x - 8)² + (y + 6)² = 5² , that is
(x - 8)² + (y + 6)² = 25
The slope-intercept equation is y=mx+b.
The slope formula is
Our three points are (5,5), (-5,-7) and (0,-1)
Using our slope formula our slope becomes
Then, if we use one of our points (pick whichever you want, although (0,1) is the easiest) to solve the equation. So, . When we solve for x and y, we get -1=0+b, or b=-1.
When we plug that back into the equation, we get.