3 years ago

What is an equation of a circle whose center is (1,4) and diameter is 10?

Mathematics

1 answer:

nexus9112 [7]3 years ago

6 0

Answer:

$x^{2} - 2x + y^{2} - 8y = 8$

Step-by-step explanation:

Standard form for a circle is:

$(x - h)^{2} + (y - k)^{2} = r^{2}$ (h, k) is the center r is the radius

$(x - 1)^{2} + (y - 4)^{2} = 5^{2} \\x^{2} - 2x + 1 +y^{2} - 8y + 16 = 25\\x^{2} - 2x + y^{2} - 8y = 8$ $x^{2} - 2x + y^{2} - 8y = 8$

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This composite shape is a rectangle with a semicircle attached on one end. The diameter of the semicircle is 6 feet.

Ugo [173]

As we can see on the picture we have a rectangle and half of circle.

The areas for half circle and rectangle are:

$A_{rectangle}=a\cdot b \\A_{halfcircle}=\frac{A_{circle}}{2}=\frac{\pi r^2}{2}$

The area of the figure is the sum of the area of half circle and rectangle. Also the height of a rectangle (6ft) is a diameter of a half circle therefore the radius of half circle is 6ft ÷ 2 = 3ft.

Now we calculate the areas.

$A_{rectangle}=10\cdot 6=\underline{60} \\A_{halfcircle}=\frac{3.14\cdot3^2}{2}=\underline{14.13} \\A_{total}=A_{rectangle}+A_{halfcircle} =60+14.13=\boxed{74.13\approx74}$