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3 years ago

Which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?

Mathematics

1 answer:

Daniel [21]3 years ago

8 0

The correct answer is: (x + 2)^2 + (y - 1)^2 = 25

Step-by-step explanation:

Given

Point on circle = P = (-5,-3)

Centre = C = (-2,1)

The distance between C and P is the radius of circle.

So,

$CP = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\= \sqrt{(-5+2)^2+(-3-1)^2}\\=\sqrt{(-3)^2+(-4)^2}\\= \sqrt{9+16}\\=\sqrt{25}\\=5\ units$

Hence,

r = 5 units

The general form of equation of circle is:

$(x-h)^2+(y-k)^2 = r^2$

Here (h,k) are the coordinates of circle

(h,k) = (-2,1)

Putting the values in standard equation

$(x-(-2))^2+(y-1)^2 = (5)^2\\(x+2)^2+(y-1)^2 = 25$

Hence,

The correct answer is: (x + 2)^2 + (y - 1)^2 = 25

Keywords: Circle, equation of circle

Learn more about equation of circle at:

#LearnwithBrainly

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Enter the equation of the line in slope-intercept form.

vitfil [10]

Answer:

y= $\frac{1}{4}$ x

Step-by-step explanation:

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3 years ago

Choose the equation that represents the graph below: (1 point) Graph of a line passing through points 0 comma 6 and 9 comma 0 y

aleksklad [387]

Answer:

Option C is correct.

Equation of a line $y=\frac{-2}{3}x+6$ passing through (0,6) and (9,0).

Explanation:

Given the two points (0, 6) and (9 ,0).

To find the equation for the given two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is,

$y-y_{1}=m(x-x_{1})$ ; where m is the slope and is given by:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

First find the slope m:

$m=\frac{0-6}{9-0} =\frac{-6}{9} =\frac{-2}{3}$

Substitute this value in equation of line:

$y-6=\frac{-2}{3} (x-0)$ or

$y-6=\frac{-2}{3} x$

⇒ $y=\frac{-2}{3}x+6$

Therefore, the equation for the given point is: $y=\frac{-2}{3}x+6$

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3 years ago

A family is driving from Phoenix to San Francisco. On a map grid, Phoenix is located at (–12, –16), and San Francisco is located

makkiz [27]

The answer is 34.05

The total distance (D) is the sum of three distances (d1, d2, and d3).

The distance formula is $d = \sqrt{(x2-x1)^{2} +(y2-y1)^{2}}$

Distance 1: Phoenix (–12, –16) to Blythe (–20, –9):
 $d1 = \sqrt{(-20-(-12))^{2} +(-9-(-16))^{2}} =\sqrt{(-20+12)^{2} +(-9+16)^{2}} \\ =\sqrt{(-8)^{2} +(7)^{2}}= \sqrt{64+49} = \sqrt{113}= 10.63$

Distance 2: Blythe (–20, –9) to Los Angeles (–33, –4):
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Distance 3: Los Angeles (–33, –4) to San Francisco (–36, 5)
 $d3 = \sqrt{(-36-(-33))^{2} +(5-(-4))^{2}} =\sqrt{(-36+33)^{2} +(5+4)^{2}} \\ =\sqrt{(-3)^{2} +(9)^{2}}= \sqrt{9+81} = \sqrt{90}= 9.49$

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3 years ago

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y=107/32

Make y the subject of formula

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Therefore,blue is

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