Question

a. An ellipse is formed by stretching the graph of x^2+ y^2=1 horizontally by a factor of 3 and vertically by a factor of 4. Determine the equation of the ellipse in standard form

x^2/a^2+y^2/b^2=1
(x/3) ^2+ (y/4) ^2=1
x^2/9 + y^2/16 =1

so the equation is:
x^2/9 + y^2/16 =1

b. The ellipse in question above is translated 4 units to the right and 2 units down. Determine the equations of this ellipse. Express your answer in both standard form and general form:

so the equation for standard form is:
(x-h)^2/a^2 + (y-k)^2/b^2=1

so
a: 9
b: 16
x: ?
Y?
h=4
k: 2

(x-4) ^2/9^2 + (y-2)^2/16^2=1

is this standard form right or am I wrong?