一个ll GRE Subject Test: Math Resources
Example Questions
Example Question #1 :Conic Sections
Using the information below, determine the equation of the hyperbola.
Foci:and
Eccentricity:
General Information for Hyperbola:
Equation for horizontal transverse hyperbola:
Distance between foci =
Distance between vertices =
Eccentricity =
Center: (h, k)
First determine the value of c. Since we know the distance between the two foci is 12, we can set that equal to.
Next, use the eccentricity equation and the value of the eccentricity provided in the question to determine the value of a.
Eccentricity =
Determine the value of
Determine the center point to identify the values of h and k. Since the y coordinate of the foci are 4, the center point will be on the same line. Hence,.
Since center point is equal distance from both foci, and we know that the distance between the foci is 12, we can conclude that
Center point:
Thus, the equation of the hyperbola is:
Example Question #11 :Conic Sections
Using the information below, determine the equation of the hyperbola.
Foci:and
Eccentricity:
General Information for Hyperbola:
Equation for horizontal transverse hyperbola:
Distance between foci =
Distance between vertices =
Eccentricity =
Center: (h, k)
First determine the value of c. Since we know the distance between the two foci is 8, we can set that equal to.
Next, use the eccentricity equation and the value of the eccentricity provided in the question to determine the value of a.
Eccentricity =
Determine the value of
Determine the center point to identify the values of h and k. Since the y coordinate of the foci are 8, the center point will be on the same line. Hence,.
Since center point is equal distance from both foci, and we know that the distance between the foci is 8, we can conclude that
Center point:
Thus, the equation of the hyperbola is:
Example Question #61 :Functions And Graphs
Find the coordinate of intersection, if possible:and.
To solve for x and y, set both equations equal to each other and solve for x.
Substituteinto either parabola.
The coordinate of intersection is.
Example Question #4 :Hyperbolas
Find the intersection(s) of the two parabolas:,
Set both parabolas equal to each other and solve for x.
Substitute both values ofinto either parabola and determine.
The coordinates of intersection are:
and
Example Question #5 :Hyperbolas
Find the points of intersection:
;
To solve, set both equations equal to each other:
To solve as a quadratic, combine like terms by adding/subtracting all three terms from the right side to the left side:
This simplifies to
Solving by factoring or the quadratic formula gives the solutionsand.
Plugging each into either original equation gives us:
Our coordinate pairs areand.
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