How do you write the equation of an ellipse with center at #(2,-3)# the major axis is vertical and is 10 units long, and the minor axis is 4 units?

1 Answer
Mar 11, 2018

Answer:

#(x-2)^2/4 + (y+3)^2/25 = 1#

Explanation:

Given: vertical ellipse with center:#(2, -3)#, major axis #= 10#, minor axis #= 4#

vertical axis ellipse equation: #(x-h)^2/b^2 + (y-k)^2/a^2 = 1#

#" where center"= (h, k); a = ("major axis")/2; b = ("minor axis")/2#

#a = 10/2 = 5; " "a^2 = 25#; #" "b = 4/2 = 2; " "b^2 = 4#

#h = 2; " " k = - -3 = +3#

vertical axis ellipse equation: #(x-2)^2/4 + (y+3)^2/25 = 1#