Question

Show that the point (0,3+√5) lies on the ellipse with foci (2,3) and(-2,3) and semi-major axis 3.

Answer 1

Solution:

$the\; ellipse\;\;\frac{(x-x_0)^2}{a^2}+\frac{(y-y_0)^2}{b^2}=1;\\x_0=0;y_{0}=3;then\\\frac{(x-0)^2}{a^2}+\frac{(y-3)^2}{b^2}=1;\\c=2;b^2=a^2-c^2=5;\\\frac{(x-0)^2}{9}+\frac{(y-3)^2}{5}=1;the\; point (0;\;3+√5);\\\frac{(0-0)^2}{9}+\frac{(3+\sqrt5-3)^2}{5}=1;\\1=1\\Answer:\\the\; point\; (0,3+√5)\; lies\; on \;the \;ellipse$