maren17

17.10.2020 •

Mathematics

PLEASE HELP THIS IS DUE SOON
Indicate whether or not each real number is rational.
.

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Ответ:

margaret8800

29.04.2022

Mathematics

The correct option is 1.

Step-by-step explanation:

The given equation of the circle is

x^2+4x+y^2-6y=-4

It can be written as

(x^2+4x)+(y^2-6y)+4=0

If we have an expression x^2+bx , then we have to add $(\frac{b}{2})^2$ to make it perfect square.

In first parenthesis the value of b is 4 so we will add (2)^2 .

In second parenthesis the value of b is -6 so we will add (-3)^2 .

(x^2+4x+2^2)+(y^2-6y+(-3)^2)+4-2^2-(-3)^2=0

(x+2)^2+(y-3)^2+4-4-9=0 $[\because (a+b)^2=a^2+2ab+b^2)]$

(x+2)^2+(y-3)^2-9=0

Add 9 on both the sides.

(x+2)^2+(y-3)^2=9

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

The standard form of the circle is

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

Where, (h,k) is center and r is radius.

From (1) and (2), we get

h=-2,k=3, r=3

Therefore the center is located at (-2, 3), and the radius is 3. Option 1 is correct.

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PLEASE HELP THIS IS DUE SOON Indicate whether or not each real number is rational. .