Respuesta :
according to the question
given data in the question,
the foci of an ellipse are (5,0) and (-5,0)
and vertices are (8,0) and (-8,0)
** Standard Form of an Equation of an Ellipse is
where Pt (h k) is the center. (a variable positioned to correspond with major axis)
a and b are the respective vertices distances from center
and are the foci distances from center: a > b
Recommend sketching it...Foci (-5,0) (5,0) and Vertices (8,0) (-8,0).
then using √(64+b^2 )=5 to find b
64 - b^2 = 25, b = √ 39
**** The standard form of the equation is an ellipse
where Pt (h, k) is the center. (variable aligned to match long axis)
a and b are the respective vertex distances from the center.
and are the distances from the center to the focal point.
a > b
hyperbolic equations in normal form,
C (h, k) and 2b units up and down from the centre at vertex 'b' Horizontal axis length
Focus units up and down from the center along x = h
& asymptotes straight line through C (h, k) with slope m = b/a
after that.
C (h, k) and corner 'a' are units left and right of the center, 2a is the length of the horizontal axis
The focal points are units left and right of the center along y = k.
asymptotes straight line through C (h, k) with slope m = b/a
parabolic vertex form open to the top (a>0) or bottom (a<0 x=removed>0) or left (a<0),
where (h, k) is the vertex and y = k is the line of symmetry.
The standard form is where the focus is (h + p, k )
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** Standard Form of an Equation of an Ellipse is
where Pt (h k) is the center. (a variable positioned to correspond with major axis)
a and b are the respective vertices distances from center
and are the foci distances from center: a > b
Recommend sketching it...Foci (-5,0) (5,0) and Vertices (8,0) (-8,0).
then using √(64+b^2 )=5 to find b
64 - b^2 = 25, b = √ 39
**** The standard form of the equation is an ellipse
where Pt (h, k) is the center. (variable aligned to match long axis)
a and b are the respective vertex distances from the center.
and are the distances from the center to the focal point.
a > b
hyperbolic equations in normal form,
C (h, k) and 2b units up and down from the center at vertex 'b' Horizontal axis length
Focus units up and down from the center along x = h
& asymptotes straight line through C (h, k) with slope m = b/a
after that.
C (h, k) and corner 'a' are units left and right of the center, 2a is the length of the horizontal axis
The focal points are units left and right of the center along y = k.
asymptotes straight line through C (h, k) with slope m = b/a
parabolic vertex form open to the top (a>0) or bottom (a<0 x=removed>0) or left (a<0),
where (h, k) is the vertex and y = k is the line of symmetry.
The standard form is where the focus is (h + p, k )
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The equation of the ellipse with foci as (5,0) and (-5,0) is
[tex]\frac{x^2}{49}+\frac{y^2}{24}=1[/tex]
What is an ellipse simple definition?
A plane section of a right circular cone that is a closed curve is produced by a point moving in such a way that the sum of its distances from two fixed points is a constant.
How do you know if an equation is an ellipse?
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 is the equation in standard form for a conic section. Here, A, B, C, D, E, and F are all real integers, and A 0, B 0, and C 0. The conic section is an ellipse if B2 - 4AC 0.
where the center is Pt(h,k). (a variable placed such that it lines up with the main axis)
The relative vertices' distances from the center are a and b.
the foci's separations from the center are: a > b
It's suggested that you sketch it: Vertices (-7,0), Focus (-5,0), and (5,0). (7,0).
then finding b
when 49 - b2 = 25.
The relative vertices' distances from the center are a and b.
furthermore,
the foci's separations from the center are: a > b
The equation for an opening up and down hyperbola
having C(h,k), vertices "b" units up and down from the center, and a transverse axis length of 2b.
Foci
29 units away from the center, along x = h
& Asymptotes Lines Through C(h,k), Slope m = b/a
Equation of a Hyperbola Opening Right and Left Standard Form:
with C(h,k), vertices 'a' units to the right and left of the center, and 2a the transverse axis length
y = k along 29 units to the right and left of the center
& Asymptotes Lines through C(h,k), slopes m = b/a
is the vertex form of a Parabola with an opening up (a>0) or down (a0).
where the vertex is (h,k), and the line of symmetry is (x = h).
The conventional form is with (h,k + p) as the main focus.
the vertex form of a Parabola opening right(a>0) or left(a0).
where y = k is the Line of Symmetry and (h,k) is the vertex
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