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Nikolay [14]
3 years ago
10

The standard form of the equation of a circle is (x−3)2+(y−1)2=16.

Mathematics
2 answers:
____ [38]3 years ago
8 0
Use:(a-b)^2=a^2-2ab+b^2\\\\(x-3)^2+(y-1)^2=16\\\\x^2-2\cdot x\cdot3+3^2+y^2-2\cdot y\cdot1+1^2=16\\\\x^2-6x+9+y^2-2y+1=16\\\\x^2+y^2-6x-2y+10=16\ \ \ |-16\\\\\boxed{x^2+y^2-6x-2y-6=0}
mash [69]3 years ago
6 0

Answer:

General Form: x^2+y^2-6x-2y-6=0

Option 1 is correct.

Step-by-step explanation:

The standard form of the equation of a circle is (x−3)²+(y−1)²=16

The general form of circle: x²+y²+2gx+2fy+c=0

Formula:

(a-b)^2=a^2-2ab+b^2

(x-3)^2+(y-1)^2=16

x^2-6x+9+y^2-2y+1=16

x^2+y^2-6x-2y-6=0

General Form: x^2+y^2-6x-2y-6=0

Standard form: (x-3)^2+(y-1)^2=16

Hence, The General Form: x^2+y^2-6x-2y-6=0

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Answer:

q = \frac{8}{3}

Step-by-step explanation:

The point of intersection (3, 1 ) is the solution to both equations

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y = qx - 7 and substituting x = 3, y = 1

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8 = 3q ( divide both sides by 3 )

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3 years ago
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Step-by-step explanation:

Refer to the picture that given :)

4 0
3 years ago
Read 2 more answers
Match the information on the left with the appropriate equation on the right.
zaharov [31]

Answer:

See attachment below

Step-by-step explanation:

For the first option, we are given m = - 2 / 3, b = 3. This is likely in the point - slope form y = mx + b, where m = slope and b = y - intercept. Thus, the equation of the line in point - slope form given this information, should be y = - 2 / 3x + 3. It seems as if none of the following equations match this form, so let us interchange the equation a bit,

y = - 2 / 3x + 3,

y + 2 / 3x = 3,

2x + 3y = 9 - Option C

_______________________________________________________

Next we are given m = - 3 / 2, and that this line passes through the point ( 4, - 1 ). Substitute m as - 3 / 2, x as 4, y as - 1, knowing point ( 4, - 1 ), into the form y = mx + b - solving for b.

- 1 = ( - 3 / 2 )( 4 ) + b,

b = 5,

Thus the equation in point - slope form should be y = - 3 / 2x + 5. None of the choices match this, so let us again alter the equation,

y = - 3 / 2x + 5,

2y = - 3x + 10,

- 2y = 3x - 10 - Option A

_______________________________________________________

( 6, 3 ) and ( 3, 1 ) is given to lie on this line. The slope of the line should be as follows,

Slope = 3 - 1 / 6 - 3 = 2 / 3

Now let us determine the y - intercept ( b ) by substitute one of the points, say ( 6, 3 ). In this case x = 6, and y = 3,

3 = ( 2 / 3 )( 6 ) + b,

b = - 1,

y = 2 / 3x - 1 = Option D

Take a look at the attachment below for further help;

6 0
3 years ago
What is the equation of the line that passes through the point (-3,4) and has a slope of 1?​
yKpoI14uk [10]

Answer:

Y=x + 7

slope = 1, the coefficient of the x term, an implicit one

plug the point y=4, x=-3 into the equation, 4=-3+7 = 4, it passes through the point (-3,4)

Step-by-step explanation:

hope it help

8 0
2 years ago
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