I need help figuring out the points you need to sketch. Any help would be appreciated.
in Calculus Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer



I presume that k(x,y)=c so 4(x+1)²-5y²-1=c for the values given.

When c=-1 we get the crossed lines part of the graph shown in green. These are asymptotes for the other two hyperbolas. The equations of the hyperbolas (or straight lines) can be found by substituting c=-1, 15 and 20. The graphs represent cross-sections of the 3-dimensional shape defined by k at various points along the z-axis where z=k(x,y). This axis can be imagined as pointing directly at the viewer, so you are looking along the axis through the 3D shape as if it were transparent. The centre of the hyperbolas and the intersection of the lines are all on the same axis where x=-1 and y=0, because in 3D a point becomes an axis. The red hyperbola corresponds to c=15 and the blue to c=20. The red hyperbola passes through the points (1,0), (-3,0), (2,2), (-4,2), (2,-2), and (-4,-2).

by Top Rated User (663k points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
83,225 questions
88,062 answers
4,947 users