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First, we are going to rewrite it as a parabola equation.
Rewrite.
Divide by 8.
Factor out coefficient.
Then, we are going to convert x into square form.
Convert the whole expression into square form.
Simplify.
Subtract 6 from both sides.
Divide by coefficient.
Rewrite in standard form.
The radius of the circle will be -2. Also, no matter what the sign says, the radius has to always be positive.
Have a nice day! :)
Rewrite.
Divide by 8.
Factor out coefficient.
Then, we are going to convert x into square form.
Convert the whole expression into square form.
Simplify.
Subtract 6 from both sides.
Divide by coefficient.
Rewrite in standard form.
The radius of the circle will be -2. Also, no matter what the sign says, the radius has to always be positive.
Have a nice day! :)
ANSWER
EXPLANATION
Since the directrix is
the axis of symmetry of the parabola is parallel to the y-axis.
Again, the focus being,
also means that the parabola will open upwards.
The equation of parabola with such properties is given by,
where
is the vertex of the parabola.
The directrix and the axis of symmetry of the parabola will intersect at
The vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix.
This implies that,
and
The equation of the parabola now becomes,
Thus, the distance between the vertex and the directrix.
This means that,
Since the parabola opens up, we choose
Our equation now becomes,
This simplifies to
or
This is the same as,
The correct answer is D .
EXPLANATION
Since the directrix is
the axis of symmetry of the parabola is parallel to the y-axis.
Again, the focus being,
also means that the parabola will open upwards.
The equation of parabola with such properties is given by,
where
is the vertex of the parabola.
The directrix and the axis of symmetry of the parabola will intersect at
The vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix.
This implies that,
and
The equation of the parabola now becomes,
Thus, the distance between the vertex and the directrix.
This means that,
Since the parabola opens up, we choose
Our equation now becomes,
This simplifies to
or
This is the same as,
The correct answer is D .