The rectangular piece of property measures 8 mi by 6 mi. find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides

The equation of ellipse is .

Step-by-step explanation:

Consider the provided information.

The rectangular piece of property measures 8 mi by 6 mi.

It is a vertical ellipse.

So, use the equation:

Where the value of a and b are:

The major axis is along y-axis with the vertices (0,4) and (0,-4).

The minor axis is along the x-axis, with the vertices (-3,0) and (3,0).

Now substitute the value of a and b in

Hence, the equation of ellipse is .

b. astronomers

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.