(x+5)^2/25+y^2/64=1

Question

Given the equation: (x+5)^2/25+y^2/64=1 find: 

a: The Center C

b: Length of Major Axis

c: Length of Minor Axis

d: Distance from C to foci c

Answer 1

with the standard form of the equation for an ellipse, you should be able to answer these questions

 

(x - h)² + (y - k)² = 1     this is for a vertical major axis (occurs when the number under the variable y is

    b²            a²                     larger than the number under the variable x)

 

(h , k) are the coordinates of the center C

 

2a is the length of the major axis (the major axis is always the longer one)

2b is the length of the minor axis

the vertex points along the vertical (major axis) are (h , k+a) and (h, k-a)

the foci coordinates are (h , k + c) and (h , k - c)

The distance c from the center to the foci is given by the equation    c² = a² - b²

 

From the equation in this question, h = -5, k = 0, a = 8, b = 5, c = √39

 

Therefore center is (-5 , 0)

length of major axis is 16

length of minor axis is 10

distance from C to foci is √39