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Airida [17]
3 years ago
14

What is the standard form of the equationCenter (-14,5), circumference: 22π

Mathematics
1 answer:
IRISSAK [1]3 years ago
6 0

The standard equation for a circle with center at (h,k) and radius r is

(x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle.

The formula for the circumference of a circle is C = 2pi*r.  In this particular problem, we need to determine the radius of the circle.  That radius is:  r = C/[2pi].  Here, C = 22pi, so we get r = 22pi/[2pi], and so r^2 = 11^2.

Putting to use the given info, we have:

(x+14)^2 + (y-5)^2 = 11^2

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Step-by-step explanation:

Let us revise the reflection and translation of a function

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f(x) = x² is the blue curve

g(x) is its image is the red curve

∵ g(x) is the image of f(x)

∵ f(x) is opened upward

∵ g(x) is opened downward

→ That means the sign of y-coordinates of all points on the blue

   graph are opposite

∴ f(x) is reflected about the x-axis

∴ Its image is - f(x)

∵ The vertex of f(x) is (0, 0)

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→ That means the function translated 4 units down

∴ - f(x) is translated 4 units down

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∴ g(x) = - f(x) - 4

∵ f(x) = x²

∴ g(x) = - x² - 4

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