find the ellipse 3

Question

given the ellipse whose eq. is 9x^2+ 16y^2- 36x+96y+36=0
FIND
A. coordinates of its center
b. semi major axis
c. semi minor axis
d. foci
e. length of the latus ******

4. find
a. vertices
b. foci
c. eccentricity
d. latus ******
e. the eq of the assymptotes
OF EACH OF THE FF HYPERBOLAS

 

Answer 1

To change the expressions (x ²- 4x) and (y ²+6y) into a perfect square trinomial,

add (half the x coefficient)² and add (half the y coefficient)²to each side of the equation.

Compare it to standard form of horizontal ellipse is

(a) Center

(b) a = semi-major axis = 4,

(c) b  = semi-minor axis = 3.

Answer 2

Continue..

(d )

(e) Latus rectum is L = 2b ²/a

= 2(9)/4 = 4.5.