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Define asymotote and explain the relationship between a hyperbola and its asymptotes?
An asymptote of a curve is a line where the distance of the curve and line approach zero as they tend to infinity (they get closer and closer without ever meeting)
If one zooms out of a hyperbola, the straight lines are usually asymptotes as they get closer and closer to a specific point, yet do not reach that point.
The asymptotes of a curve are straight lines such that, as one of the curve's coordinates becomes infinitely large, the curve comes infinitesimally close to the line without ever reaching it.
A hyperbola has two asymptotes which intersect at its centre of symmetry. These divide the coordinate plane into four segments and the two arms of the hyperbola are contained within diagonally opposite segments.
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How can you know if a graph represents a proportional relationship?
It is a relationship of direct proportion if and only if the graph is a straight line which passes through the origin. It is an inverse proportional relationship if the graph is a rectangular hyperbola. A typical example of an inverse proportions is the relationship between speed and the time taken for a journey.
What is the relationship between the coupon rate and the YTM for premium bonds?
klk
What is the mathematical relationship between joules and calories?
1 cal= 4.18 J
What is the relationship between exponential and logarithmic functions?
Exponential and logarithmic functions are inverses of each other.
How do you tell between a parabola and a circle by just looking at their equations?
The equations for any conic section (which includes both parabolas and circles) can be written in the following form: Ax^2+Bxy+Cy^2+Dx+Ey+F=0 Some terms might be missing, in which case their coefficient is 0. The way to figure out if the equation is a parabola, circle, ellipse, or hyperbola is to look at the value of B^2-4AC: If it's negative, the graph is an ellipse (of which a circle is a special case). If it's 0, the graph is a parabola. If it's positive, the graph is a hyperbola. The special case of a circle happens when B is 0 -- there is no "xy" term -- and A=C.
There is a relationship between the in the hyperbola's equation and the equations for the hyperbola's asymptotes?
denominators
What is the relationship between the hyperbola equation and the equation for the hyperbola asymptotes?
If the equation of a hyperbola is ( x² / a² ) - ( y² / b² ) = 1, then the joint of equation of its Asymptotes is ( x² / a² ) - ( y² / b² ) = 0. Note that these two equations differ only in the constant term. ____________________________________________ Happy To Help ! ____________________________________________
There is a relationship between the denominators in the hyperbola's equation and the equations for the hyperbola's?
denominators
How does an increase in eccentricity affect the shape of a hyperbola?
Hyperbolae with different eccentricities have a different angle between their asymptotes.
What mathematical relationship between variables is suggested by a graph showing a hyperbola?
Inverse
What is observed in a scatter-plot that has an inverse relationship between x and y?
A right hyperbola shape.
What is the major difference between the equation for a hyperbola and for an ellipse?
ellipse are added hyperbola are subtracted
What major difference between the equation for a hyperbola and for an ellipse is the operation performed The terms in the equation of an are subtracted?
hyperbola
What is the difference between hyperbola and parabola?
A parabola has eccentricity 1, a hyperbola has eccentricity greater than 1.
The major difference between the equation for a hyperbola and for an ellipse is the operation performed The terms in the equation of are added?
hyperbola
The length of a hyperbola's transverse axis is equal to the the distances from any point on the hyperbola to each focus?
difference between
The length of a hyperbola's transverse axis is equal to the the distances from any point on the hyperbola to each focus.?
difference between
