The tangent is perpendicular to the radius which joins the centre of the circle to the point P. As the tangent is a straight line, the equation of the tangent will be of the form y = m x + c.

2. Consider a tangent of the curve \ (y=17-2x^2\) that goes through the point \ ( (3,1)\text {.}\) Provide a diagram of this situation. Can you draw two tangent lines? Find the slopes of those tangent ...

5. Find an equation of the tangent line to the curve \ (x=t-t^ {-1}\text {,}\) \ (y=1+t^2\) at \ (t=1\text {.}\) ...

But there's a trick that uses calculus and the magic of dividing by zero. Instead of finding the tangent line, it's much easier to find the slope of a line that touches the curve at two points.

The tangent is perpendicular to the radius which joins the centre of the circle to the point P. As the tangent is a straight line, the equation of the tangent will be of the form y = m x + c.