All SAT II Math II Resources
Example Question #1 : Graphing Functions
Note: Figure NOT drawn to scale.
Refer to the above figure. The circle has its center at the origin; the line is tangent to the circle at the point indicated. What is the equation of the line in slope-intercept form?
Insufficient information is given to determine the equation of the line.
A line tangent to a circle at a given point is perpendicular to the radius from the center to that point. That radius, which has endpoints , has slope
The line, being perpendicular to this radius, will have slope equal to the opposite of the reciprocal of that of the radius. This slope will be . Since it includes point , we can use the point-slope form of the line to find its equation: