Question

Q10 Q3.) Find the standard form of the equation of the ellipse satisfying the given conditions.

Answer 1

ellipse center (0,0) so its eqn is x^2/a^2 + y^2/b^2 = 1
major axis is horizontal n length 18
so at y=0, x=+/-18
a=18
minor axis is vertical n length 2
so at x=0, y=+/-2
b=2

ans is (x/18)^2 + (y/2)^2 = 1

Answer 2

Given horizontal axis length is larger than the vertical axis length, the standard form of an ellipse is:

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

where (h,k) is center; a and b are the major and minor axis

(h,k) = (0,0) and a=18, b=2

(x/18)^2 + (y/2)^2 = 1 is the standard form equation