Find the standard equation for the ellipse, using the given characteristic or characteristics. vertices:(0,+-7) foci: (0,+-√33)

Answer:[tex]=\frac{x^2}{16} +\frac{y^2}{49}=1[/tex]Step-by-step explanation:The equation of this ellipse is [tex]\frac{(x-h)^2}{b^2} +\frac{y-k)^2}{a^2} =1[/tex]for a vertical oriented ellipse where;(h,k) is the centerc=distance from center to the focia=distance from center to the verticesb=distance from center to the co-verticesYou know center of an ellipse is half way between the vertices , hence the center (h,k) of this ellipse is (0,0) and its is vertical oriented ellipseGiven thata= distance between the center and the vertices, a=7c=distance between the center and the foci, c=√33Then find b[tex]a^2-b^2=c^2\\\\b^2=a^2-c^2\\\\\\b^2=7^2-(\sqrt{33} )^2\\\\\\b^2=49-33=16\\\\\\b^2=16[/tex]The equation for the ellipse will be[tex]\frac{(x-0)^2}{16} +\frac{(y-0)^2}{49} =1\\\\\\=\frac{x^2}{16} +\frac{y^2}{49} =1[/tex]