A circle is a set of points in a plane equidistant
from a fixed point. It has a general formula of x² + y² = r². This is if the
center is at the origin. However, if the center at point h and k, the
equation becomes (x-h)² + (y-k)² = r².<span>
We write the given equation in the
form (x-h)² + (y-k)² = r² by completing the square.
</span>
<span>x</span>²<span> + y</span>²<span> + 10x – 6y + 18 = 0</span>
<span>
(x² + 10x + 25 )+ (y² - 6y + 9) = −18 + 25 + 9 = 16
(x + 5)² + (y + 3)² = (4)²
Therefore,
center = (-5, -5)
radius = 4</span>
A
First, I’m going to the line is question into slope intercept form.
y + 10 = -5x + 5
y = -5x + 5 -10
y = -5x -5
y + 10 = -5 (x - 1) becomes y = -5x -5 in slope intercept form. I will call this line ‘line 1’
A becomes y = 5x -15 in slope intercept form
B becomes y = -5x + 25 in slope intercept form
C becomes y = -5x -5 in slope intercept form
D becomes y = -5x + 10 in slope intercept form
C is the same line as line 1. Any point that is on line 1 is also on line C, so C cannot be it.
Notice that line B and D have the same slope but different y-intercepts as line 1. That means these lines are parallel (not the same line though - different y intercepts) to line 1, so they will never intercept.
Line A has a different slope vs line 1, so they will eventually intersect only once
The answer to the solution of the equation 5x+2y=-1 is 1,-3)
