Parabolas and Circles - SAT Subject Test in Math I
Card 0 of 5
Give the axis of symmetry of the parabola of the equation
Give the axis of symmetry of the parabola of the equation
The line of symmetry of the parabola of the equation
is the vertical line
Substitute 
:
The line of symmetry is
That is, the line of the equation 
.
The line of symmetry of the parabola of the equation
is the vertical line
Substitute
The line of symmetry is
That is, the line of the equation
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What is the center of the circle with the following equation?
What is the center of the circle with the following equation?
Remember that the basic form of the equation of a circle is:
This means that the center point 
is defined by the two values subtracted in the squared terms. We could rewrite our equation as:
Therefore, the center is 
Remember that the basic form of the equation of a circle is:
This means that the center point
Therefore, the center is
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What is the area of the sector of the circle formed between the 
-axis and the point on the circle found at 
when the equation of the circle is as follows?
Round your answer to the nearest hundreth.
What is the area of the sector of the circle formed between the
Round your answer to the nearest hundreth.
For this question, we will need to do three things:
- Determine the point in question.
- Use trigonometry to find the area of the angle in question.
- Use the equation for finding a sector area to finalize our answer.
Let us first solve for the coordinate by substituting into our equation:
Our point is, therefore: 
Now, we need to calculate the angle formed between the origin and the point that we were given. We can do this using the inverse tangent function. The ratio of 
to 
is here: 
Therefore, the angle is:
To solve for the sector area, we merely need to use our standard geometry equation. Note that the radius of the circle, based on the equation, is 
.
This rounds to 
.
For this question, we will need to do three things:
- Determine the point in question.
- Use trigonometry to find the area of the angle in question.
- Use the equation for finding a sector area to finalize our answer.
Let us first solve for the coordinate by substituting into our equation:
Our point is, therefore:
Now, we need to calculate the angle formed between the origin and the point that we were given. We can do this using the inverse tangent function. The ratio of
Therefore, the angle is:
To solve for the sector area, we merely need to use our standard geometry equation. Note that the radius of the circle, based on the equation, is
This rounds to
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What is the area of the sector of the circle formed between the 
-axis and the point on the circle found at 
when the equation of the circle is as follows?
Round your answer to the nearest hundreth.
What is the area of the sector of the circle formed between the
Round your answer to the nearest hundreth.
For this question, we will need to do three things:
- Determine the point in question.
- Use trigonometry to find the area of the angle in question.
- Use the equation for finding a sector area to finalize our answer.
Let us first solve for the coordinate by substituting into our equation:
Our point is, therefore: 
Now, we need to calculate the angle formed between the origin and the point that we were given. We can do this using the inverse tangent function. The ratio of 
to 
is here: 
Therefore, the angle is:
To solve for the sector area, we merely need to use our standard geometry equation. Note that 
, based on the equation, is 
.
This rounds to 
.
For this question, we will need to do three things:
- Determine the point in question.
- Use trigonometry to find the area of the angle in question.
- Use the equation for finding a sector area to finalize our answer.
Let us first solve for the coordinate by substituting into our equation:
Our point is, therefore:
Now, we need to calculate the angle formed between the origin and the point that we were given. We can do this using the inverse tangent function. The ratio of
Therefore, the angle is:
To solve for the sector area, we merely need to use our standard geometry equation. Note that
This rounds to
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If the center of a circle is at 
and it has a radius of 
, what positive point on the 
does it intersect?
If the center of a circle is at
Since you are looking for a point on the 
, your 
value will be zero.
The center of the circle is at the origin and radius is the distance from the center, so that means the point you are looking for must be 
points away from 
.
This can be two points on the 
but since you are looking for a positive one, your answer must be 
.
Since you are looking for a point on the
The center of the circle is at the origin and radius is the distance from the center, so that means the point you are looking for must be
This can be two points on the
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