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Korvikt [17]
3 years ago
9

What is the equation of the circle with center (−3, 1) that passes through the point (−5, 3)?

Mathematics
1 answer:
Mariulka [41]3 years ago
6 0

Answer:

( x + 3)^2 + ( y - 1)^2 = 8

Step-by-step explanation:

The equation of a circle with a center and a point

( x - a) ^2 + ( y - b) ^2 = r^2

( x , y) - any point on the circle

( a, b) - center of the circle

r^2 - radius of the circle

( -3 , 1) - center - ( a, b)

a = -3

b = 1

( -5 , 3) - point - ( x, y)

x = -5

y = 3

Step 1: substitute the center into the equation

( x -(-3)^2 + ( y - 1)^2 = r^2

( x + 3)^2 + ( y - 1)^2 = r^2

Step 2 : sub the point into the equation

( x + 3)^2 + ( y - 1)^2 = r^2

( -5 + 3)^2 + ( 3 - 1)^2 = r^2

(-2)^2 + 2^2 = r^2

4 + 4 = r^2

8 = r^2

Step 3 : sub the radius into the equation

( x + 3)^2 + ( y - 1)^2 = r^2

( x + 3)^2 + (y - 1)^2 = 8

Therefore, the equation of the circle is

( x + 3)^2 + (y - 1)^2 = 8

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Answer:

Let say 75% of  cars older than age  = Y  years

than 25 % cars of age less than Y Years

Z score corresponding to 25 %  =  -0.674

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Value = Y

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SD = 3.2

Z score = -0.674

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3 years ago
The coordinates of the vertices of a regular polygon are given. Find the area of the polygon to the nearest tenth.
alexandr1967 [171]

Answer:

The area is equal to 8\ units^{2}

Step-by-step explanation:

we have

A(0, 0), B(2, -2), C(0, -4), D(-2, -2)

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The figure is a square (remember that a regular polygon has equal sides and equal internal angles)

see the attached figure

The area of the square is

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AB=\sqrt{(-2-0)^{2}+(2-0)^{2}}

AB=\sqrt{(-2)^{2}+(2)^{2}}

AB=\sqrt{8}

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<u><em>Find the area of the square</em></u>

A=(2\sqrt{2})^{2}

A=8\ units^{2}

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