Question 383613: Write the equation of the line tangent to circle x2 + y2 = 25 at the point (-4,3) A line is tangent to a circle if it is perpendicular to a line through the center of the circle at the point in which this line meets the circle
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! Write the equation of the line tangent to circle x2 + y2 = 25 at the point (-4,3) A line is tangent to a circle if it is perpendicular to a line through the center of the circle at the point in which this line meets the circle
x^2 + y^2 = 25
center is (0,0)
point (-4,3) --> -4^2 + 3^2 = 16 + 9 = 25, (-4,3) is on the circle
slope-intercept form of line is y = mx + b, b is the y-intercept
(vertical intercept)
m = slope of line = rise/run = (y2 - y1)/(x2 - x1) = (-4 - 0)/(3 - 0)
m = -4/3, this is slope of the line passing through the center,
the perpendicular line will be the negative reciprocal of -4/3 or 3/4
the tangent line is y = (3/4)x + b, need to determine what b is
plug in (-4,3):
3 = (3/4)(-4) + b
3 = -3 + b
6 = b
tangent line is y = (3/4)x + 6
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