Answer:
[tex]\frac{x^{2} }{36}+\frac{y^{2} }{16}=1[/tex]
Step-by-step explanation:
As we know standard equation of n ellipse is [tex]\frac{(x-0)^{2} }{(-6)^{2}}+\frac{(y-0)^{2} }{(4)^{2} }=1[/tex]
In the given equation (h, k) is the center, a is the vertex and b is the co-vertex.
Here vertex is (-6, 0) and co-vertex is (0, 4)
Therefore, length of a = -6, b = 4 and origin is (0, 0)
Now the equation of the ellipse will be
[tex]\frac{(x-0)^{2} }{(-6)^{2}}+\frac{(y-0)^{2} }{(4)^{2} }=1[/tex]
[tex]\frac{x^{2} }{6^{2}}+\frac{y^{2} }{4^{2} }=1[/tex]
[tex]\frac{x^{2} }{36}+\frac{y^{2} }{16}=1[/tex]
Therefore, the equation of the ellipse will be [tex]\frac{x^{2} }{36}+\frac{y^{2} }{16}=1[/tex]
