all of number 3 please Find the center, vertices, and foci of the ellipse Then,

Question

all of number 3 please Find the center, vertices, and foci of the ellipse Then, sketch each ellipse. Find the center, vertices, and foci. Write the equations of the asymptotes of each hyperbola Then, sketch each hyperbola. Find the vertex, the focus, and the directrix of the parabola x^2 - 2x + 8y + 9 = 0 Find the center, vertices, and foci of an ellipse: 9x^2 + 25y^2 - 36x - 50y + 60 = 0 Find the center, vertices, and foci of a hyperbola. Then, write the equations of the asymptotes. x^2 - 9y^2 + 2x- 54^y -71=0 Write the equation of A parabola with its vertex,(0, 4), and its directrix y = 2 An ellipse with foci (0, 0) and (0,8). Its major axis of length 16 A hyperbola with the vertices (0,2), and (6,2) and the equations of the asymptotes are y = (2/3)x and y = 4 - (2/3)x

Explanation / Answer

(2)Ellipse

comparing the cofficent with the given equation

a= 13 , b = 12

also sqrt(a^2-B^2) = sqrt (169-144) = 5

therefor cordinates of foci = (-c,0) and (c,0) are (-5,0) and (5,0)

vertices = (-a,0) and (a,0) = (-13,0) and (13,0)

the dinominator of x^2 > dinominator of y^2

so the foci of the ellipse are on the x - axis lets a = 13 , b = 12

Ecentricity = c / a = 5/13

Answer

(3) calculate the vertices , foci and center of hyperbola

x^2 - y^2 = 4

devided the given eqn by 4 we got

x^2/4 - y^2/4 = 1

comparing the eqn

a = 2 , b = 2

c = sqrt(a^2 +b^2) = 2

cordinates of foci (+-2,0)

the vertices are (+-4,0)

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