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Find an equation in traditional develop for the hyperbola via 0 votes
vertices at (0, ±2) and also foci at (0, ±7).hyperbolaaskedJul 11, 2013in PRECALCULUSby homeworkhelpMentor
You are watching: Find an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±11).
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General equation of a hyperbola
We have foci and also vertices are on the y-axis, which suggests that we demands the formula for a up and also down hyperbola.
This suggests that the facility (h, k) must be a the origin, or (0, 0). So, let"s label that...
h = 0k = 0
We understand that "a" is the distance from your vertex and "c" is the distance from your foci
a = 2 and also c = 7
We have a formula that
Now fill that
h = 0
k = 0
Therefore the required equation of hyperbola is
The vertices of the hyperbola are (0, 2) and (0, - 2) and its foci are (0, 7) and (0, - 7).
Due to the fact that the x - coordinate isconstantin theverticesandfoci, this is a vertical hyperbola.
The traditional create of vertical hyperbola (y - k)2/a2 - (x - h)2/b2 = 1.Wbelow, "b " is the number in the denominator of the positive term, If the x - term is negative, then the hyperbola is vertical.a = semi - transverse axis , b = semi - conjugate axis .Center: (h, k )Vertices: (h , k + a ) and also (h, k - a).Foci: (h , k +c) and (h, k - c).
So, the x coodinate of the center of hyperbola is 0.
vertices : (0, 2) and also (0,- 2)
k + a = 2 ----> (1)
k - a = - 2 ---> (2)
Add the equations (1) & (2).
2k = 0
⇒ k = 0
So,the y coordinate of center is 0.
Substitute the k worth in (1),
0 + a = 2
⇒ a = 2.
foci : (0, 7) and (0, - 7)
k + c = 7
0 + c = 7
c = 7
c2 = a2 + b2
(7)2 = (2)2 + b2
49 - 4 = b2
b = √45
Substitute the (h , k), a, and b in traditional form of hyperbola equation .
(y - 0)2/22 - (x - 0)2/(√45)2 = 1
(y - 0)2/4 - (x - 0)2/45 = 1.
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Because of this, the standard create of hyperbola is (y - 0)2/4 - (x - 0)2/45 = 1.answeredAug 5, 2014by lillyExpert Please log in or register to include a comment. Related questionsWrite the equation in conventional develop for the hyperbola through vertices (4,0) & (-4,0) and asymptote y=(1/4)x &?askedFeb 5, 2013in PRECALCULUSby homeworkhelpMentorhyperbola Find the equation for the hyperbola with facility at the origin, one vertex at (6, 0), and a focus at (10, 0).askedSep 9, 2014in CALCULUSby tonymatePupilcalculusequation-of-a-hyperbolafoci-of-a-hyperbolavertex-of-a-hyperbolahyperbola Find the equation of the hyperbola whose vertices are at (-1, -5) and (-1, 1) via a emphasis at (-1, -7)?askedMay 16, 2013in PRECALCULUSby mathgirlApprenticehyperbola Find equation for hyperbola?askedMay 1, 2013in PRECALCULUSby mathgirlApprenticehyperbola Graph the hyperbola with equationaskedJul 6, 2013in PRECALCULUSby dkinzApprenticehyperbola Find the Center,foci, and also vertices of the hyperbola, and sketch its graph using asymptotes as an help.askedFeb 17, 2015in CALCULUSby anonymouscenterverticesfociasymptoteshyperbola Write the equation of a hyperbola with foci at (-1, 1) and also (5, 1) and also vertices at (0, 1) and (4, 1).askedJul 7, 2014in ALGEBRA 2by anonymousequation-of-a-hyperbolavertex-of-a-hyperbolahyperbolavertices-foci-and-asymptotes-in-hyperbolasfoci-of-a-hyperbola what is the length of the transverse axis of hyperbola defined by the equation?askedJul 6, 2013in PRECALCULUSby rockstarApprenticehyperbola Find an equation in conventional form for the ellipse with the vertical significant axis of length 16 and also minor axis of length 10.askedDec 12, 2018in CALCULUSby anonymouscalculus Find an equation in traditional form for the ellipse through the vertical significant axis of size 18, and minor axis of size 6.askedAug 7, 2014in CALCULUSby Tdog79Pupilcalculus Precalculus Help???? Graph the hyperbola????askedJul 24, 2014in PRECALCULUSby heatherApprenticeequation-of-a-hyperbolahyperbola Find the vertices, foci, and asymptotes of the hyperbola and also sketch its graph.askedFeb 2, 2015in CALCULUSby anonymousverticesfociasymptoteshyperbola for the conic y=5x^2-40x+78 discover an equation in conventional create and also its vertex, emphasis, and directrixaskedNov 30, 2013in ALGEBRA 2by lindaScholarconic-sectionstandard-develop Find an equation for the hyperbola through vertices at (0, -6) and (0, 6);askedNov 12, 2014in PRECALCULUSby anonymousequation-of-a-hyperbola Find an equation for the hyperbola with?askedNov 11, 2014in PRECALCULUSby anonymousequation-of-a-hyperbolaequation-of-parabola Find the typical form of the equation of the hyperbola via the offered qualities.askedFeb 2, 2015in TRIGONOMETRYby anonymousstandard-form-hyperbola Find the traditional form of the equation of the hyperbola through the offered qualities.askedFeb 2, 2015in TRIGONOMETRYby anonymousstandard-form-hyperbola Find the typical develop of the equation of the hyperbola with the provided qualities and center at the beginning.askedFeb 2, 2015in TRIGONOMETRYby anonymousstandard-form-hyperbola Find the conventional develop of the equation of the hyperbola via the offered qualities and facility at the beginning.askedFeb 2, 2015in TRIGONOMETRYby anonymousstandard-form-hyperbola What is the equation for Y=-3x-7 in traditional form through integer coefficients and also exactly how did you find it.askedMar 4, 2013in ALGEBRA 1by abstain12Apprenticestandardformslope-intercept