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mazolethrin6876
27.07.2019 •
Mathematics
The equation of a hyperbola is x2 − 4y2 − 2x − 15 = 0. the width the asymptote rectangle is units, and its height is units.
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Ответ:
Before we get into what the h, k, a and b represent, let’s get the equation we are given into standard form.
First we pull aside the terms that have x in them. These are
This is still not in standard form. Let’s move the constant term (the number -15) to the right hand side. We get:
Notice that the equation in standard form is equal to 1 but ours is equal to 16. So we divide every term by 16 and this yields:
It is almost in standard form. In standard form the denominators are written
This finally gives the equation in standard form. It is:
Comparing this to the standard form we see h=1 and k=0. This is the center of the hyperbola (h,k) which is (1,0).
The denominator of the first fraction gives the value a which here is 4. Twice this value is the length of the rectangle used to find the asymptotes. That is, the length of the asymptotic rectangle is 8.
The denominator of the second fractions gives the value b which here is 2. Twice this value is the width of the rectangle used to find the asymptotes. that is, the width of the asymptotic rectangle is 4.
Though you are not asked to graph this hyperbola. The diagonals of the rectangle would help us draw it as they would give the asymptotes.
Ответ:
you can simplify rations just like you simplify fractions. Whenever you are able to evenly divide both parts of the ratio with out changing the equation's answer, you are able to.
for example
if it were 3:6, you can simplify this by dividing these both by 3, leaving you with 1:2.