All categories

4 years ago

Identify this conic section. x 2 - 4x + y 2 - 4y + 4 = 12 line circle ellipse parabola hyperbola

Mathematics

2 answers:

ANTONII [103]4 years ago

7 0

Answer: The answer is (B) circle.

Step-by-step explanation: The given equation of the conic section is

$x^2-4x+y^2-4y+4=12.$

We are to select the correct type of the conic section from the given options.

Let us try to find the standard form of the given conic section as follows:

$x^2-4x+y^2-4y+4=12\\\\\Rightarrow (x^2-4x+4)+(y^2-4y+4)=12+4\\\\\Rightarrow (x-2)^2+(y-2)^2=16\\\\\Rightarrow (x-2)^2+(y-2)^2=4^2.$

Therefore, the given conic section is a circle with centre (2, 2) and radius 4 units.

The image of the circle is shown in the attached figure.

Thus, (b) Circle is the correct option.

Stells [14]4 years ago

4 0

The coefficients for the x² and the y² is the same, with the same sign, namely is +1 for both, and when that happens, what we have is a circle.

You might be interested in

Which equations are true? Choose all answers that apply: Choose all answers that apply: (Choice A) A -x +0+(- x) = 0−x+0+(−x)=0m

lora16 [44]

Answer:

(B)-x-(-x) =0

Step-by-step explanation:

<u>Option A</u>

Our equation is: -x +0+(- x) = 0

Left Hand Side:

-x +0+(- x) = -x-x=-2x

$($Left Hand Side) $-2x\neq 0$ (Right Hand Side)$

<u>Option B</u>

Our equation is: -x-(-x) =0

Left Hand Side:

-x-(-x) =-x+x=0

$($Left Hand Side) 0 = 0 (Right Hand Side)$

Therefore, the equation in Option B is true.

3 0

4 years ago

The equation for this question.

just olya [345]

We can solve this by setting up a system of equations. We will use x for the $3 boxes and y for the $5 boxes:

x+y=34
3x+5y=130

We can use the elimination method by multiplying the first equation by 3:

3x+3y=102
3x+5y=130

0x-2y=-28
y=14

We can then plug this number back into one of the original equations to solve for x:

x+14=34
x=20

We can check these answers by plugging them into the equations:

20+14=34
34=34

(3)(20)+(5)(14)=130
60+70=130
130=130

Therefore, there are 20 of the $3 boxes, since we originally said that x would be the $3 boxes.

8 0

4 years ago

9 is greater than x, and -6 is less than x

Nastasia [14]

This is what I got but lmk if it not right

3 0

3 years ago

Jack is 3 times as old as lacy. 3 years ago the sum of there ages was 14. How old are they now?

Elan Coil [88]

Answer:

lacy = 8 jack= 24

Step-by-step explanation:

let x be lacys age

3x - 3 + x-3 = 14

3x+x -3 = 14 + 3 = 17

4x = 17 +3 = 20

x = 20/4 = 5

lacys age now = 5+3 = 8

jacks age now = 8 * 3 = 24

3 0

3 years ago

The surface area of a rectangular prism is 32 square inches. The volume of the prism is 12 cubic inches. The sum of all edge len

Goryan [66]

Answer:

36 cubic inches.

Step-by-step explanation:

Let the length, width and height of the rectangular prism are a, b, c respectively.

So, surface area, 2(ab + bc + ca) = 32 {Given} ............ (1)

Volume, abc = 12 {Given} ............ (2)

And, the sum of all the edges, 4(a + b + c) = 28 {Given} .......... (3)

Now, if the length width and height are increased by 1 inch, then the volume of the prism will be = (a + 1)(b + 1)(c + 1)

= abc + (ab + bc + ca) + (a + b + c) + 1

= 12 + 16 + 7 + 1 {From equations (1), (2) and (3)}

= 36 cubic inches. (Answer)

3 0

4 years ago