Write down the equation of an ellipse in standard form.

Question

ellipse; length of LR = 3, minor axis coincides

with the vertical diameter of the circle (x - 2)2+ (y+9)2= 8

Answer 1

(x-h)^2/a^2 + (y-k)^2/b^2 where (h,k)=ellipse's center, a= half the horizontal axis, b = half the vertical axis

(x-2)^2 + (y+9)^2 = 8 is a circle with center (2,-9) and radius = sqr8= 2sqr2, diameter=4sqr2

vertical diameter is on the line x=2 from (2,-9-2sqr2) to (2,-9+2sqr2)

if the ellipse's minor axis coincides with the circle's vertical diameter, and is equal to the vertical diameter, then the minor axis is also from (2,-9-2sqr2) to (2,-9+2sqr2) and b=2sqr2, (h,k) = (2,-9)

the ellipse's equation is

(x-2)^2/a^2 + (y+9)/8 = 1, where a^2>8 such as 9. since a= half the major axis of the ellipse

Latus Rectum = LR=3 = chord through the focus = 2b^2/a = 3, a =2b^2/3 = 2(8)/3, a^2 = (16/3)^2= 256/9

9(x-2)^2/256 + (y+9)^2/8 = 1

(no guarantees this solution is error(s) free)