Question

Find the length of the portion of the line y = 4 that lies inside a circle of radius 7
centered at the origin

Answer 1

Answer: 2sqrt(33)

Step-by-step explanation:

We want to find the length of the line y = 4 in the circle x^2+y^2=49.

Substitute y = 4 to get x^2 = 33, so x = sqrt(33) or -sqrt(33).

That means the total length is sqrt(33) * 2 = 2sqrt(33).

Hope that helped,

-sirswagger21

Answer 2

The approximate length of the portion of the line is 11.49.

Circle centered at (h,k) with radius r is  $(x-h)^{2} + (y-k)^{2}=r^{2}$

A circle of a radius 7 centered at the origin:

$x^{2} +y^{2}=49$   ......... (i)

$y=4$               ..........(ii)

We have a circle and a line.  We need to find the points of

intersection and find the distance between those two points.

Replace y with 4 in the 1st equation and solve for x.

$x^{2} +4^{2} =49\\x^{2} =49-16\\x^{2} =33$

$x=$ ±$\sqrt{33}$

We have the 2 values of x where the line intersects the circle.

Plug those into one of the original equations to find the associated

y values.

$\sqrt{33} ^{2} +y^{2} =49\\y^{2}=49-33\\y=4$

Two points on the circle are $(\sqrt{33} , 4)$ and $(-\sqrt{33} , 4)$

Using the distance formula:-

$=\sqrt{(4-4)^{2}+(-\sqrt{33}-\sqrt{33)} ^{2} } \\=\sqrt{(2\sqrt{33}) ^{2} } \\=2\sqrt{33}$

≈ 11.49

Therefore, the length of the portion of the line is approximately 11.49.

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