PRACTICE
PROBLEMS:
Give
the equation; the length of a; and the length of the focal chord for the
parabola, which is the locus of all points equidistant from the point and the
line, given in the following problems:
ANSWERS:
Up
to now, all of the parabolas we have dealt with have had a vertex at the origin
and a corresponding equation in one of the four following forms:
1.
y2 = 4ax
2.
y^{2} =  4ax
3. x2 = 4ay
4. x2 =  4ay
We
will now present four more forms of the equation of a parabola. Each one is a
standardized parabola with its vertex at point V(h,k). When the vertex is moved
from the origin to the point V(h,k), the x and y terms of the equation are
replaced by (x  h) and (y  k). Then
the standard equation for the parabola that opens to the right (fig. 29, view A) is
The
four standard forms of the equations for parabolas with vertices at the point V(h,k) are as follows:
The
method for reducing an equation to one of these standard forms is similar to
the method used for reducing the equation of a circle.
EXAMPLE:
Reduce the equation
to
standard form.
SOLUTION:
Rearrange the equation so that the seconddegree term and any firstdegree
terms of the same unknown are on the left side. Then group the unknown term
appearing only in the first degree and all constants on the right:
Then complete
the square in y:
To get the equation in the form
factor an 8 out of the right side. Thus,
is the equation of the parabola with its vertex at (1,3).
PRACTICE PROBLEMS:
Reduce the equations given in the following problems to
standard form:
ANSWERS:
