The value of a, b, c, h, k, and foci coordinates are 4, 3, 5, 2, -1, and (5, 0) and (-5, 0) respectively.
It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.
We have given a hyperbola equation:
[tex]\rm \dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1[/tex]
We know the standard form of a hyperbola is given:
[tex]\rm \dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]
After comparing:
a² = 16 ⇒ a = 4
b² = 9 ⇒ b = 3
[tex]\rm c^2 = a^2+b^2\\\\\rm c^2 = 16+9 \Rightarrow 25[/tex]
c = 5
(h, k) is the center of the hyperbola:
(h, k) = (2, -1)
Vertices will be (a, 0) and (-a, 0):
(4, 0) and (-4,0)
Foci will be at (c, 0) and (-c, 0):
(5, 0) and (-5, 0)
Thus, the value of a, b, c, h, k, and foci coordinates are 4, 3, 5, 2, -1, and (5, 0) and (-5, 0) respectively.
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The value of a=4 , b=3 , k=-1 and h=2 for the hyperbola having the equation
[tex]\dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1[/tex]
A hyperbola is the symmetrical open curve formed by the combination of a circular cone with a plane at a minimum angle with its axis than the side of the cone.
Here the general form of the equation of hyperbola will be:
[tex]\dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1[/tex]
And we have a equation given as:
[tex]\dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1[/tex]
By comparing the equation we the solutions
[tex]a=4 , b=3 , k=-1 \ and\ h=2[/tex]
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