document.write( "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 \n" ); document.write( "
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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\r
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\n" ); document.write( "\n" ); document.write( "x^2 + y^2 = 25
\n" ); document.write( "center is (0,0)
\n" ); document.write( "point (-4,3) --> -4^2 + 3^2 = 16 + 9 = 25, (-4,3) is on the circle
\n" ); document.write( "slope-intercept form of line is y = mx + b, b is the y-intercept
\n" ); document.write( "(vertical intercept)
\n" ); document.write( "m = slope of line = rise/run = (y2 - y1)/(x2 - x1) = (-4 - 0)/(3 - 0)
\n" ); document.write( "m = -4/3, this is slope of the line passing through the center,
\n" ); document.write( "the perpendicular line will be the negative reciprocal of -4/3 or 3/4
\n" ); document.write( "the tangent line is y = (3/4)x + b, need to determine what b is
\n" ); document.write( "plug in (-4,3):
\n" ); document.write( "3 = (3/4)(-4) + b
\n" ); document.write( "3 = -3 + b
\n" ); document.write( "6 = b
\n" ); document.write( "tangent line is y = (3/4)x + 6\r
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