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Rom4ik [11]
4 years ago
10

The rectangular piece of property measures 10 mi by 4 mi. find an equation for the ellipse if the path is to touch the center of

the property line on all 4 sides.
Mathematics
1 answer:
Bess [88]4 years ago
8 0
Let the center of this elipse be on the origin and let this elipse be horizontal.
major axis is 10 mi, minor axis is 4 mi
(x^2/5^2)+(y^2/2^2)=1
     (x^2/25)+(y^2/4)=1
            4x^2+25y^2=100
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Answer:

x=16\dfrac{28}{37}\\ \\y=5\dfrac{1}{3}\\ \\z=7.5

Step-by-step explanation:

The diagram shows three paralel lines which divide the large triangle into three similar triangles.

By Thales theorem,

\dfrac{5}{z}=\dfrac{y}{8}=\dfrac{2}{3}

Then

\dfrac{5}{z}=\dfrac{2}{3}\Rightarrow 2z=15,\ z=7.5\\ \\\dfrac{y}{8}=\dfrac{2}{3}\Rightarrow 3y=16,\ y=\dfrac{16}{3}=5\dfrac{1}{3}

From the similarity of triangles,

\dfrac{x}{20}=\dfrac{z+8}{z+8+3}\\ \\\dfrac{x}{20}=\dfrac{7.5+8}{7.5+8+3}\\ \\\dfrac{x}{20}=\dfrac{15.5}{18.5}\\ \\x=20\cdot \dfrac{155}{185}=20\cdot \dfrac{31}{37}=\dfrac{620}{37}=16\dfrac{28}{37}

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The point-slope form of the equation of the line that
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