Question

Find the coordinates of the focus and the vertex, the equations of the directix and the axis, and the lendth of the latus rectum of the parabola `y^(2)=-12x`

Answer 1

The given equations is of the form `y^(2)=-4ax"where "4a=12,i.e. a=3` This is a left-handed parabola, Its focus is `F(-a,0),i.e. F(-3,0)` Its vertex is O(0,0) The equation of the directrix is x=a i.e, x=3. Its axis is x-axis, whose equations is y=0. Length of latcus rectum=`4a=(4xx3)`units=12units.