If the major axis is horizontal and has a length of 22 units, the minor axis has a length of 18, and the ellipse has a Center C of (-7,6), fill in the missing denominators for the equation and determine the distance from C to the foci(c). (x + 7)^2 + (y - 6)^2 = 1 Denominator , Denominator , Distance from C to foci ___________, ___________, ___________
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The general equation for an ellipse with horizontal major axis is `y = (x - h)^2/a^2 + (y-k)^2/b^2`
The value of a = 11 as that is the distance from the center (-7, 6) to a vertex. The value of b is 9 as that is the distance to a co-vertex since the center.
This means that `a^2 = 11^2 = 121` and `b^2 = 9^2 = 81.`
Therefore, the denominators are 121 and 81, respectively.
The distance from C to foci can be found by `F =sqrt(a^2 - b^2).`
"a" represents the semi-major axis and "b" represents the semi-minor axis.
`F =sqrt(11^2 - 9^2)`
`F =sqrt(121-81)`
`F =sqrt(40)` = `2sqrt(10)` ≈ `6.325`
The solutions are, the first denominator is 121, the second denominator is 81, and the distance c=from C to foci is `2sqrt(10)` or 6.325.
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