According to the information given, the equation of the elipse is:
[tex]\frac{(x - 1)^2}{25} + \frac{(y - 6)^2}{21} = 1[/tex]
The equation of an elipse of center [tex](x_0, y_0)[/tex] is given by:
[tex]\frac{(x - x_0)^2}{a^2} + \frac{(y - y_0)^2}{b^2} = 1[/tex]
In this problem, the center is (1,6), hence [tex]x_0 = 1, y_0 = 6[/tex].
There is a vertex at (6,6), hence [tex]a = 6 - 1 = 5[/tex].
The focus at (-1,6) means that [tex]c = 1 - (-1) = 2[/tex], hence:
[tex]c^2 = a^2 - b^2[/tex]
[tex]b^2 = a^2 - c^2[/tex]
[tex]b^2 = 5^2 - 2^2[/tex]
[tex]b^2 = 21[/tex]
The equation is:
[tex]\frac{(x - 1)^2}{25} + \frac{(y - 6)^2}{21} = 1[/tex]
A similar problem is given at https://brainly.com/question/25072920
