Write the general equation of ellipse with the center at the origin, foci have coordinates 0,4 and 0, -4 and one of the vertex is at 0, -5?
- MathguyLv 51 month ago
you have a vertical ellipse.... F1( 0, -4 ) F2( 0, 4 ) V1( 0, - 5)
eqn: ( x - h )^2 / b^2 + ( y - k )^2 / a^2 = 1
c^2 = a^2 - b^2
h = k = 0 since center is origin
so a = 5 since vertex is 5 units away from the center, and foci are 4 units from center, so c = 4 length of ellipse is 2a
what is b^2 ? b represents the " 1/2 width" from the center left, right of the center.
[ width would be 2b ....... 2b or not 2b, that is the question .... ? sorry, couldn't resist :) ]
4^2 = 5^2 - b^2 I'll let you solve for b^2
you have it all... a, so calculate a^2 , b^2 h,k = 0 in this problem, and put them into your equation.