Hey guys, I've tried this one a few times and just can't seem to get it. Help would be appreciated:
A circle has its center at C(4,8). A point Q(12,6) is on the circumference of the circle. A tangent line to the circle is drawn at point Q. Determine the equation of the tangent line.
Draw a diagram. Note the fact that the angle between the tangent and the radius is 90 degrees. Use this fact, geometry and some simple trigonometry to get the angle that the tangent makes to the x-axis. Then .
Knowing the gradient of a line and a point on it, you should be able to get the equation of the line.
You might also use the fact that if the lines corresponding to and are perpendicular, then . You know that a radius passing through (4, 8) and (12, 6). What is the slope of that line? You know that the tangent at (12, 6) is perpendicular to that radius so you can find the slope of the tangent. Now you know the slope and one point of the line so you can find the equation of the line.