Find the equation of the given conic. Horizontal ellipse with center (5, 1),major Diameter=10 and minor Diameter=8.

Question

Find the equation of the given conic. Horizontal ellipse with center (5, 1),major Diameter=10 and minor Diameter=8.

Answer 1

(x-5)^2/25 +(y-1)^2/16 = 1

that's probably the answer you want

or eliminate fractions

16(x-5)^2 + 25(y-1)^2 =400

or multiply it out, expand, combine constant terms

16(x^2 -10x +25) + 25(y^2 -2y +1) = 400

16x^2 -160x +400 + 25y^2 -50y +25 = 400

16x^2 -160x +25y^2 =-25

or convert to polar coordinates, x=rcoxT, y=rsinT

(rcosT-5)^2/25 + (rsinT -1)^2/16 = 1

(x-h)^2/a^2 +(y-k)/b^2 = 1

where (h,k) = (5,1) = the center

a= 10/2=5 = half major axis

b = 8/2 = 4 = half minor axis