As the tangent is a straight line, the equation of the tangent will be of the form \(y = mx + c\). We can use perpendicular gradients to find the value of \(m\), then use the coordinates of P to find ...

To find the tangent line to a curve at a point P we first pick another point on the curve a little bit away from P. Call this point Q. Do this below by clicking "Another Point". Then connect these two ...

The Mathematical Gazette is the original journal of the Mathematical Association and it is now over a century old. Its readership is a mixture of school teachers, college and university lecturers, ...

Sketch the graph of the ellipse \(\ds \frac{x^2}{9}+\frac{y^2}{16}=1\) and determine its foci. Let \(C\) be the conic which consists of all points \(P=(x,y)\) such ...

There are three ways a line and a circle can be associated, ie the line cuts the circle at two distinct points, the line is a tangent to the circle or the line misses the circle. To work out which ...