What is the equation of the circle with center (2, –5) that passes through the point (–2, 10)?
1 answer:
The standard equation of a circle is
(x-h)^2 + (y-k)^2 = r^2
where the center is at point (h,k)
From the statement of the problem, it is already established that h = 2 and k = -5. What we have to determine is the value of r. This could be calculated by calculating the distance between the center and point (-2,10). The formula would be
r = square root [(x1-x2)^2 + (y1-y2)^2)]
r = square root [(2--2)^2 + (-5-10)^2)]
r = square root (241)
r^2 = 241
Thus, the equation of the circle is
(x-h)^2 + (y-k)^2 = r^2
where the center is at point (h,k)
From the statement of the problem, it is already established that h = 2 and k = -5. What we have to determine is the value of r. This could be calculated by calculating the distance between the center and point (-2,10). The formula would be
r = square root [(x1-x2)^2 + (y1-y2)^2)]
r = square root [(2--2)^2 + (-5-10)^2)]
r = square root (241)
r^2 = 241
Thus, the equation of the circle is
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Considering the definition of perpendicular line, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is .
A linear equation o line can be expressed in the form y = mx + b.
where
- x and y are coordinates of a point.
- m is the slope.
- b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.
Perpendicular lines are lines that intersect at right angles or 90° angles.
Two nonvertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. In other words, if you multiply the slopes of two perpendicular lines, you get –1.
<h3>Equation of perpendicular line in this case</h3>In this case, the line is 3x+y=-9. Expressed in the form y = mx + b, you get: y= -9 - 3x or, what is the same, y= -3x -9
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of -3. So:
(-3)× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-3)
<u><em>slope perpendicular line= </em></u>
Finally, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is .
Learn more about perpendicular line:
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