the correct question is
What is the equation in standard form of an ellipse centered at the origin and vertex (4,0) and focus (1,0)
we know that
Standard form of equation for an ellipse with horizontal major axis is
(x-h)²/a²+(y-k)²/b²=1
the center is the origin
so
(h,k) is (0,0)length of horizontal major axis------> 8=2a-----> a=4
a²=16
c=1 (distance from center to focal point)
c²=1
b²=a²-c²-----> b²=16-1----> b²=15
the equation is
(x)²/16+(y)²/15=1
the answer is
(x)²/16+(y)²/15=1
