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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, ±2) and foci at (0, ±7)?
Solution:
Given:
Vertices at (0, ±2) and foci at (0, ±7)
As both vertices and foci lie on the y-axis
Equation of hyperbola is y2/b2 - x2/a2 = 1
Vertices = (0, ±2)
b = 2
Foci = (0, ±7)
be = 7
Eccentricity e = 7/2
We know that,
e = √(1 + a2/b2)
Substituting the values
7/2 = √(1 + a2/b2)
Squaring on both sides
49/4 = 1 + a2/b2
⇒ a2/b2 = 49/4 - 1
⇒ a2/b2 = 45/4
Here,
a2 = 45/4 × 22
⇒ a2 = 45/4 × 4
⇒ a2 = 45
⇒ a = 3√5
So the equation of hyperbola is
y2/4 - x2/45 = 1
Therefore, the equation of hyperbola in standard form is y2/4 - x2/45 = 1.
Find an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±7)?
Summary:
An equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±7) is y2/4 - x2/45 = 1.
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