Find the area of the circle whose equation is x2+y2=6x-8y

Mathematics

1 answer:

Semenov [28]3 years ago

6 0

Answer:

Given that the equation of a circle is :

$\green{ \boxed{\boxed{\begin{array}{cc} {x}^{2} + {y}^{2} = 6x - 8y \\ = > {x}^{2} + {y}^{2} - 6x + 8y = 0 \\ = > {x}^{2} + {y}^{2} + 2 \times ( - 3) \times x + 2 \times 4 \times y = 0 \\ \\ \sf \: standard \: equation \: o f \: circle \: is : \\ {x}^{2} + {x}^{2} + 2gx + 2fy + c = 0 \\ \\ \sf \: by \: comparing \\ \\ g = - 3 \\ f = 4 \\ c = 0 \\ \\ \sf \: radius \: \: r = \sqrt{ {g}^{2} + {f}^{2} - c } \\ = \sqrt{ {( - 3)}^{2} + {4}^{2} - 0 } \\ = \sqrt{9 + 16} \\ = \sqrt{25} \\ = 5 \: unit \\ \\ \bf \: area \: = \pi {r}^{2} \\ = \pi \times {5}^{2} \\ =\pink{ 25\pi \: { unit }^{2} }\end{array}}}}$

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The following table shows the number of feet a bird flies above the ground as a function of time: (In the picture)

Otrada [13]

Answer:

D.) (14, 0); the time it takes for the bird to reach the ground

Step-by-step explanation:

The attached graph shows a plot of the table values and the two offered solution options.

The dependent variable in this scenario is the bird's height above the ground. When that is zero, the bird is on the ground. This fact makes choices B and C seem ridiculous.

We note from the table and graph that the bird is on a path that decreases in height by 3 feet every 2 seconds. If the bird continues that rate of descent, it will reach the ground after 14 seconds.

That is, its (time, height) pair will be (14, 0), matching choice D.

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Choosing any answer to this question requires making assumptions that are inconsistent with real-world bird behavior. At least, the problem statement should say what assumptions are applicable.