Degenerate Conic What value of must be if the graph of the equation
is an ellipse, a single point the empty set
The value of for which the graph of the equation is an ellipse.
The given equation is
Take , and … (1)
Then the equation is an ellipse if
Compare the equation with the general second-degree equation of an ellipse
Then, , , , and .
From equation (1)
Substitute the values, , , , and
The value of for which the graph of the equation is a single point.
The value of has to be greater than for the given equation to represents an empty set.
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