Given the elipse 4x^2 + 9y^2 + 32x - 144y + 604 = 0 Find: a) The Center b) Length of Major Axis c) Length of Minor Axis d) Distance from C to foci
Given equation of ellipse is:
`4x^2 + 9y^2 + 32x - 144y + 604 = 0`
Rewrite the equation in the form:
Divide both sides by 36,
This is the standard equation of a horizontal ellipse.
1. Its center C is at (-4,8).
2. To determine the length of the major axis, consider the larger denominator which is 9.
length of major axis = 2a=2*3=6 units.
3. Similarly, `b^2=2^2`
length of minor axis = 2b=2*2=4 units.
4. To find the distance of the foci from the center of the ellipse, apply the formula:
Plugging in the values of `a^2` and `b^2`
c=`sqrt(9-4) =sqrt5` units.
Hence, the distance of each focus from the center of the ellipse is `sqrt5` units.