MATH 215 MIDTERM 1 HELPFUL INFO
EXAM QUESTIONS WITH COMPLETE
SOLUTIONS
Circle - ANSWERSx^2 + y^2 = r^2
Sphere - ANSWERSx^2 + y^2 + z^2 = r^2
Cylinder - ANSWERSx^2 + y^2 = r^2 ; z is unconstrained
Ellipse - ANSWERS(x^2)/(a^2) + (y^2)/(b^2) = 1
What is the general equation of an ellipsoid? - ANSWERS(x^2)/(a^2) + (y^2)/(b^2) +
(z^2)/(c^2) = 1
In the equation of an ellipsoid, what is the condition for x, y, and z? - ANSWERSAll x, y,
z are on one side of the equation and positive, all squared.
What is the condition for all terms in the cone equation? - ANSWERSAll terms are
squared
Equation of Tangent Plane/Linear Approximation/Differentials - ANSWERSz-z0 =
fx(x0,y0)(x-x0) + fy(x0,y0)(y-y0)
Elliptic Paraboloid - ANSWERS(x^2)/(a^2) + (y^2)/(b^2) = z/c ; The not squared variable
is the axis along which the shape lies, two variables positive on one side, one positive
on the other
Hyperbolic Paraboloid/Saddle - ANSWERS(x^2)/(a^2) - (y^2)/(b^2) = z/c ; one variable
is not squared, there is one negative sign
What is the equation of a cone in standard form? - ANSWERS(x^2)/(a^2) + (y^2)/(b^2) =
(z^2)/(c^2)
What is the alternative equation of a cone? - ANSWERS(x^2)/(a^2) + (y^2)/(b^2) -
(z^2)/(c^2) = 0
In the equation of a cone, what is the sign of z? - ANSWERSNegative on the same side
In the equation of a cone, how are the terms x and y related? - ANSWERSThey have
matching signs
Hyperboloid of One Sheet - ANSWERS(x^2/a^2) + (y^2/b^2) - (z^2/c^2) = 1
EXAM QUESTIONS WITH COMPLETE
SOLUTIONS
Circle - ANSWERSx^2 + y^2 = r^2
Sphere - ANSWERSx^2 + y^2 + z^2 = r^2
Cylinder - ANSWERSx^2 + y^2 = r^2 ; z is unconstrained
Ellipse - ANSWERS(x^2)/(a^2) + (y^2)/(b^2) = 1
What is the general equation of an ellipsoid? - ANSWERS(x^2)/(a^2) + (y^2)/(b^2) +
(z^2)/(c^2) = 1
In the equation of an ellipsoid, what is the condition for x, y, and z? - ANSWERSAll x, y,
z are on one side of the equation and positive, all squared.
What is the condition for all terms in the cone equation? - ANSWERSAll terms are
squared
Equation of Tangent Plane/Linear Approximation/Differentials - ANSWERSz-z0 =
fx(x0,y0)(x-x0) + fy(x0,y0)(y-y0)
Elliptic Paraboloid - ANSWERS(x^2)/(a^2) + (y^2)/(b^2) = z/c ; The not squared variable
is the axis along which the shape lies, two variables positive on one side, one positive
on the other
Hyperbolic Paraboloid/Saddle - ANSWERS(x^2)/(a^2) - (y^2)/(b^2) = z/c ; one variable
is not squared, there is one negative sign
What is the equation of a cone in standard form? - ANSWERS(x^2)/(a^2) + (y^2)/(b^2) =
(z^2)/(c^2)
What is the alternative equation of a cone? - ANSWERS(x^2)/(a^2) + (y^2)/(b^2) -
(z^2)/(c^2) = 0
In the equation of a cone, what is the sign of z? - ANSWERSNegative on the same side
In the equation of a cone, how are the terms x and y related? - ANSWERSThey have
matching signs
Hyperboloid of One Sheet - ANSWERS(x^2/a^2) + (y^2/b^2) - (z^2/c^2) = 1
