Original Source: http://tube.geogebra.org/student/mtuwhq3AH The diagram shows a line [i]L[/i] with equation [math]y=-k[/math] and a circle [i]C[/i] with equation [math]x^2+y^2=r^2[/math] The circle [i]C1[/i] with centre at [i]P[/i], is tangent to the circle [i]C[/i] and the line [i]L[/i] at [i]N[/i].
Explain why the locus of [i]P[/i] is a parabola as point [i]N[/i] varies on [i]L[/i]. State the fixed point and fixed line in this case, in terms of k and r. Write down the equation of the parabola.