Mathematics, 13.04.2020 04:13 lyrhiii

Which of the following equations are equations of circles? Choose all that apply
(x+5)2 + (y + 2)2 = -4
2x2 + y2 +15x – y + 3 = 0
x2 + y2 + 2x+10y-5=0
3x2 + 3y2 + 12x +30y - 6 = 0
x2 - y2 + 20x + 2y +9= 0

Answers: 2

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Answer from: SauceyNaee

Step-by-step explanation:

The work form of a circle is

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

The standard form of a circle is

Ax^2+Bxy+Cy^2+Dx+Ey+F=0

This standard form is a circle if A and C are the same number, there is a plus sign in between the x-squared and the y-squared terms, and the F value, when moved to the other side of the equals sign, is not negative. That F value represents the radius which is a measure of distance, and distances cannot be negative.

Looking at the first choice in your list, on the right side of the equals sign we have a negative 4. That means that that equation is not a circle.

Looking at the second choice in your list, we have a 2x^2 and a y^2, where A = 2 and C = 0. This is not a circle, either, since A and C have to be the same number in a circle, and they are not.

Looking at the third choice in your list, we have x^2 and y^2 with the same A and C value of 1, and if we move the F value of -5 over, we have a radius of 5, and there is a + sign in between the x^2 and the y^2 terms. Choice 3 is a circle.

Looking at the fourth choice, we have that A = 3 and C = 3, there is a + sign in between the x^2 and the y^2 terms, and if we move the -6 over to the other side, the radius is a positive number. Choice 4 is also a circle.

Looking at the last choice, there is a - sign in between the x^2 and the y^2 terms. Even though A and C are both the same number, 1, the - sign makes that possibly a hyperbola, but definitely NOT a circle.

Answer from: Quest

Answer: the correct answer is 10step-by-step explanation: let the number be n, then the expression becomes,then“twelve more than the quotient of a number and two, decreased by four” is $(\frac{n}{2}+12)-4$ when n=4,we substitute 4 whetever we see n to get, $(\frac{4}{2}+12)-4$ we simplify to obtain, $=(2+12)-4$ we further simplify to get, $=14-4=10$ therefore the correct answer is c.

Answer from: Quest

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

$m_ {1} * m_ {2} = - 1$

then, given the following line:

$6x-3y = 18\\6x-18 = 3y$

$\frac {6x} {3} - \frac {18} {3} = y\\y = \frac {6x} {3} - \frac {18} {3}\\y = 2x-6$

so, $m_ {1} = 2$

we are looking for m_ {2}:

$m_{2}=\frac{-1}{m_{1}}\\m_{2}=\frac{-1}{2}\\m_{2}=-\frac{1}{2}$

then, the line is given by:

$y = - \frac {1} {2} x + b$

we find "b" replacing the given point:

$8 = - \frac {1} {2} (0) + b\\8 = b$

finally, the equation is:

$y = - \frac {1} {2} x + 8$

option c

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Which of the following equations are equations of circles? Choose all that apply
(x+5)2 + (y +...

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