Question

a eBook 10.1.052 Find the equations of two distinct ellipses satisfying the given conditions. Center at (3, -6); major axis of length 11; minor axis of length 4. +3+621 □ 121 4r -32+021 0 121 121 121 (z-32 4 +6)2 121 Need Help? Tlik to a Tutor Additional Materials La eBook

Answer 1

center (3,-6)

length of major axis =11
=>length of semimajor axis =11_/2

length of minor axis =4
=>length of semiminor axis =4_/2
=>length of semiminor axis =2

two equations of distinct ellipses :

$\\\frac{(x-3)^{2}}{(\frac{11}{2})^{2}}+\frac{(y-(-6))^{2}}{2^{2}}=1,\frac{(x-3)^{2}}{2^{2}}+\frac{(y-(-6))^{2}}{(\frac{11}{2})^{2}}=1\\ \\=>\frac{(x-3)^{2}}{\frac{121}{4}}+\frac{(y+6)^{2}}{4}=1,\frac{(x-3)^{2}}{4}+\frac{(y+6)^{2}}{\frac{121}{4}}=1\\ \\=>\frac{4(x-3)^{2}}{121}+\frac{(y+6)^{2}}{4}=1,\frac{(x-3)^{2}}{4}+\frac{4(y+6)^{2}}{121}=1\\$

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