Answer to Question #148543 in Analytic Geometry for Dhruv rawat

Question #148543
Show that the point (0,3+√5) lies on the ellipse with foci (2,3) and (-2,3) and semi major axis 3.
1
Expert's answer
2020-12-07T15:03:17-0500

The foci are (2,3) and (-2,3), so obviously (0,3) is a center and c=2. Semi major axis a=3. Therefore we can find a semi minor axis b from the formula "b^2+c^2=a^2,b=\\sqrt{a^2-c^2}=\\sqrt{9-4}=\\sqrt{5}" . We put these values in the general equation of the ellipse and we get:


"\\frac{x^2}{9}+\\frac{(y-3)^2}{5}=1"


Let's put "(0,3+\\sqrt{5})" in this equation:

"\\frac{0}{9}+\\frac{(3+\\sqrt{5}-3)^2}{5}=\\frac{(\\sqrt{5})^2}{5}=1" , which proves that this point lies on the indicated ellipse.


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