Questions (1 Viewer)

[Arithela]

1. A point P(x,y) moves so that it is equidistant from the x-axis and the point (0,3).
a) Show the locus of P is a parabola and find its equation.

2.
a) Determine the equation of the directive of the parabola 2y = (x - 1)(x - 3)
b) Find the equations of the tangents to the curve at the points where the parabola cuts the x-axis.
c) Show that these tangents meet on the directrix.

 

[aalex]

Have fun!:wave:

 

[Arithela]

thank you so much but I dont get the first line of working:

Distance from P to x-axis is : d(P, x-axis) = y

 

[aalex]

We can use the formula for the perpendicular distance from a point to a line. However, in our case it’s easier to notice that the point P has the coordinates x and y (given) and the line is x-axis (y = 0), so the distance is the length of the segment from P to the foot of the perpendicular on x-axis.
There is a rectangle formed with the coordinates of P and the x and y axes, so the distance is equal to y (opposite side in rectangle).
Still confused?

 

[Arithela]

I get it now! Thanks