find the vertices and co-vertices of x²/4+y²=25.

Question

Standard equation of an ellipse with center at the origin

Answer 1

Equation of ellipse is (x-h)^2/a^2+(y-k)^2/b^2 = 1

Given equation is x^/4+y^2 = 25

Divide to each side by 25.

x^2/4*25+y^2/25 = 25/25

x^2/100+y^2/25 = 1

x^2/10^2+y^2/5^2 = 1

Now tofind vertices and covertices

√a^2 = √100 = ±10

Vertices are (10,0) (-10,0)

 √b^2 =√25 = ±5

Covertices are (0,5)(0,-5)