Question

The standard form for an ellipse whose major axis is parallel to the x axis is:\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2}=1 Where a>b and the point (h,k) is the center of the ellipse.Write the equation below in standard form and then answer the following questions. If a value is a non-integer type your answer as a decimal rounded to the hundredths place. x^2-8x+25y^2-100y+91=0The center of the ellipse is (h,k). h= Answer and k= AnswerThe value for a is Answer . The value for b is Answer .The foci with the positive x value is the point ( Answer, Answer)The foci with the negative x value is the point ( Answer, Answer)

Answer 1

The standard form for the ellipse whose major axis

Write the equation in a standard form

`x^2-8x+25y^2-100y+91=0`
`\begin{gathered} x^2-8x_+25y-100y+91=0 \\ x^2-8x+4^2+25y^2-100y=91 \\ (x-4)^2+25(y^2-4y)=91 \\ (x-4)^2+25(y-2)^2=91+16+25(4) \\ (x-4)^2+25(y-2)^2=116-91 \\ ((x-4)^2+25(y-2)^2=25)/(25) \\ ((x-4)^2)/(25)+((y-2)^2)/(1)=1 \end{gathered}`

(1) The centre of the ellipse is (h , k)

`h=4,k=2`

(2) The value of a = 5

(3) The value of b = 1

(4) The foci with the positive x value is the points

`(0,+5)`

(5) The foci with the negative x value is the points

`(0,-5)`