use [ tex ] and [ /tex ] (remove the spaces inside the square brackets).

For example, [ tex ] x [ /tex ] gives

The equation of the tangent at any point on the parabola is given by:

Solving simultaneously the equations of the tangent and the parabola , we get

Treating this as a quadratic in , we can solve it using the quadratic formula to obtain:

Taking the midpoint and simplifying gives us the parametric equation

and it's easy to show that the equivalent Cartesian equation is .

(A nice trick you can use to find the midpoint in questions like these is to halve the sum of roots - this is most useful when you don't need the coordinates.)

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