Chapter Twenty-Two — Conic Sections
The Humongous Book of Algebra Problems
504
Note: Problems 22.31–22.32 refer to the ellipse with center (4,–1) that passes through the
origin if the major axis is horizontal and ab = 8.
22.32 Write the equation of the ellipse in standard form.
Substitute x = 0 and y = 0 into the equation from Problem 22.31 written in terms
of a.
Multiply the entire equation by the least common denominator, 64a
2
, to
eliminate fractions.
Solve the equation by factoring.
Substitute into the equation to calculate b.
The ellipse
passes through
the origin, the
point (x,y) = (0,0).
Substitute these
values into the
equation so that
the only unknown
that’s left is a.
Use the
zero product
property. The only
way (a
2
– 32)(a
2
– 32)
could equal zero is if
the factors equal
zero.
Don’t worry
about the ±
sign, because a, b,
and c are positive
values.
Chapter Twenty-Two — Conic Sections
The Humongous Book of Algebra Problems
505
Rationalize the denominator.
Substitute h = 4, k = –1, , and into the standard form equation
for an ellipse with a horizontal major axis.
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