SOLUTION: The line A has slope 3/4 and passes through the point (1,4). If the line A is tyangent to the circle whose center is at (1,2), which of the following points is on the circle?

Algebra ->  Circles -> SOLUTION: The line A has slope 3/4 and passes through the point (1,4). If the line A is tyangent to the circle whose center is at (1,2), which of the following points is on the circle?      Log On


   

Question 996945: The line A has slope 3/4 and passes through the point (1,4). If the line A is tyangent to the circle whose center is at (1,2), which of the following points is on the circle?
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
The line A is y-4=(3/4)(x-1) in point-slope form and this becomes
y=%283%2F4%29%28x-1%29%2B4
y=%283%2F4%29x-3%2F4%2B4
y=%283%2F4%29x-3%2F4%2B16%2F4
y=%283%2F4%29x%2B13%2F4-----line A as slope-intercept form.


The point of tangency ON the circle is ALSO ON line A, so this tangency point is some general unknown point with ordered pair (x,(3/4)x+13/4). Call this point T on the circle.


The slope of T and point (1,2) multiplied by the slope of line A must have a product of NEGATIVE 1, because line A and the line with T and (1,2) must be perpendicular.
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Putting that into algebra as an equation,
%283%2F4%29%28%28%283%2F4%29x%2B13%2F4-2%29%2F%28x-1%29%29=-1
.

I omit doing the rest of the solution. Examine and study all that presented and be sure this last equation makes sense. When it makes sense to you, then continue with it, to solve for x. You should expect TWO solutions, and therefore two points. Find x, and evaluate the corresponding y.