A Handy Way to Find the Equation of a Tangent Line to a Circle
Posted: April 4, 2024 in Mathematics Tags: exams, math, Mathematics, research
The DSE (click here to see what HKDSE is) is close. The math core exam is less than 2 weeks time. I am going to share a really nice equation to find the tangent of a given point on the circle. Suppose that the general form of a circle is given by
then the equation of a tangent line at point will be as follows:
Proof:
Differentiate the equation of the circle with respect to x implicitly.
hence y’ is,
then the slope of the tangent at point would be
By point slope form of a line,
Now, since the given point satisfies the circle, we plug into the circle,
Hence, we have the following,
Move everything to the left, therefore
QED. Good luck.
