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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±10).
Solution:
Standard form of the equation of a hyperbola is
(x – h)2/a2 - (y - k)2/b2 = 1
Where (h, k) is the center = (0, 0)
Distance from center to vertices
a = 9 ⇒ a2 = 81
Distance from center to vertices which is given from the foci
c = 10
⇒ c2 = 100
Using the Pythagorean formula,
c2 = a2 + b2
Substituting the values
100 = 81 + b2
So we get,
b2 = 100 - 81 = 19
Substituting the values in the standard form
x2/81 - y2/19 = 1
Therefore, the equation of the hyperbola is x2/81 - y2/19 = 1.
Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±10).
Summary:
The equation for the hyperbola with vertices at (0, ±9) and foci at (0, ±10) is x2/81 - y2/19 = 1.
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