Question

Complete the following: by the di tant to Complete the squares for each quadratic, list the center and radius, then graph each circle (a-ha r-rs-i Since the radius is an imaginary value, the equation is not a real circle. (h) x2 + y2 - 7y = 0 rº + y2 + 2mr - 2ny = 0 letter h from question 1 please

Answer 1

EXPLANATION

Given the equation x^2 + y^2 - 7y = 0

As we already know, the Ellipse Standard Equation is as follows:

`((x-h)^2)/(a^2)+((y-k)^2)/(b^2)=1`

With center (h,k) and (a,b) are the semi-major and semi-minor axes.

Rewrite x^2+y^2 -7y =0 in the form of the standard ellipse equation:

Group x-variables and y-variables together:

`x^2+(y^2-7y)=0`

Convert y to square form:

`x^2+(y^2-7y+(49)/(4))=0+(49)/(4)`

Refine 0+49/4

`x^2+(y-(7)/(2))^2=0+(49)/(4)`

Refine 0+49/4

`x^2+(y-(7)/(2))^2=(49)/(4)`

Divide by 49/4:

`(x^2)/((49)/(4))+((y-(7)/(2))^2)/((49)/(4))=1`

Rewrite in standard form:

`((x-0)^2)/(((7)/(2))^2)+((y-(7)/(2))^2)/(((7)/(2))^2)=1`

Therefore, ellipse properties are:

(h,k)=(0,7/2) a=7/2, b=7/2

b>a therefore b is semi-major axis b=7/2, semi-minor axis a=7/2

The properties of the ellipse are: center (h,k)=(0,7/2), semi-major axis b=7/2 and semi-minor axis a=7/2.

Then, the graph is: