   SEARCH HOME Math Central Quandaries & Queries  Question from Jamie, a student: Use the Greek method to find an equation of the tangent line to the circle x^2+y^2-4x+6y+4=0 at the points (3,2square root 2-3. Hi Jamie,

I don't know what you mean by the Greek method but I can show you how I would solve this problem.

First rewrite the equation as

$\left[ x^2 - 4x\right] + \left[y^2 + 6y \right] = -4.$

Next I would complete the square for each of the expressions in square brackets to get an expression of the form

$(x - a)^2 + (y - b)^2 = r^{2}.$

This is an expression for the circle with center $(a ,b)$ and radius $r.$ Thus you know the coordinates of the center of the circle.

To complete this problem use that fact that for a circle with center $O$ and a point $P$ on the circumference of the circle, the line segment from $O$ to $P$ is perpendicular to the tangent to the circle at $P.$

Write back if you have problems completing the problem. Tell us what you have done and we will try to help,
Penny      Math Central is supported by the University of Regina and the Imperial Oil Foundation.