Differentiate algebraic and trigonometric equations, rate of change, stationary points, nature, curve sketching, and equation of tangent in Higher Maths.

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.

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.