SOLUTION: What is the center, foci, and the length of the major and minor axes for the ellipse whose equation is, 16x^2 + 25y^2 + 32x

SOLUTION: What is the center, foci, and the length of the major and minor axes for the ellipse whose equation is, 16x^2 + 25y^2 + 32x - 150y = 159?

Question 28463: What is the center, foci, and the length of the major and minor axes for the ellipse whose equation is, 16x^2 + 25y^2 + 32x - 150y = 159?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
What is the center, foci, and the length of the major and minor axes for the ellipse whose equation is, 16x^2 + 25y^2 + 32x - 150y = 159?
STANDARD EQN.OF ELLIPSE IS
(X-H)^2/A^2 + (Y-K)^2/B^2 = 1
WHERE
CENTRE IS (H,K)
ECCENTRICITY = E = {(A^2-B^2)/A^2}^0.5
FOCI ARE (H+AE,K)AND (H-AE,K)
MAJOR AXIS LENGTH = 2A
MINOR AXIS LENGTH = 2B
WE HAVE
16x^2 + 25y^2 + 32x - 150y - 159 =0
{(4X)^2+2*(4X)*4+4^2}-4^2+{(5Y)^2-2*(5Y)*15+15^2}-15^2-159=0
(4X+4)^2 + (5Y-15)^2 = 400
16(X+1)^2 + 25(Y-3)^2 =400...DIVIDING BY 400 THROUGHOUT..
(X+1)^2/25 + (Y-3)^2/16 =1
(X+1)^2/5^2 + (Y-3)^2/4^2 =1
COMPARING WITH ABOVE STANDARD EQN.
CENTRE IS (-1,3)
ECCENTRICITY E IS {(25-16)/25}^0.5=3/5
FOCI ARE (-1+5*3/5 ,3) AND (-1-5*3/5,3)=(2,3) AND (-4,-3)
MAJOR AXIS LENGTH = 2*5=10
MINOR AXIS LENGTH = 2*4=8

RELATED QUESTIONS
What is the center, foci, and the lengths of the major and minor axes for the ellipse,... (answered by venugopalramana)

What is the center, foci, and the length of the major and minor axes for the ellipse... (answered by venugopalramana)

What is the center, foci, and the lengths of the major and minor axes for the ellipse,... (answered by Paul)

What is the center, foci, and the lengths of the major and minor axes for the ellipse,... (answered by venugopalramana)

How do you find the coordinates of the center and foci and the lengths of the major and... (answered by ewatrrr)

Find the center, foci, vertices, and lengths of the major and minor axes. 16x^2 - 64x (answered by lwsshak3)

1. The equation of an ellipse is given by (x+2)^2/25 + (y-1)^2/16=1 a. Give the... (answered by ewatrrr)

1. The equation of an ellipse is given by (x-3)^2/64 + (y+5)^2/100 = 1 a. Identify... (answered by Alan3354)