SOLUTION: Show that the line y = 10 − 3x is tangent to the circle x2 + y2 = 10. Find an equation for the line perpendicular to the tangent line at the point of tangency. Show that this lin
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-> SOLUTION: Show that the line y = 10 − 3x is tangent to the circle x2 + y2 = 10. Find an equation for the line perpendicular to the tangent line at the point of tangency. Show that this lin
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Question 1157994: Show that the line y = 10 − 3x is tangent to the circle x2 + y2 = 10. Find an equation for the line perpendicular to the tangent line at the point of tangency. Show that this line goes through the center of the circle. Answer by greenestamps(13209) (Show Source):
Solve the pair of equations simultaneously. If there is a single solution, then the line and the circle intersect in only one place; that means the line is tangent to the circle.
The system of equations has only one solution: x=3, which makes y=1.
So the point of tangency is (3,1). The slope of the tangent line is -3; the slope of a line perpendicular to it is 1/3. Use the point-slope form of a linear equation.
The y-intercept is 0; that means the line passes through the origin, which is the center of the circle.
