salasivis

01.10.2021 •

Mathematics

Student Activity Sheet 1; Overview 1. REVIEW Look at the patterns below. Can you find the next two items in each list and state the rule for finding them?
a. 2, 4, 6, 8, ...
b. 2, 3, 5, 9, 17, ...
c. 1, -2, 3, 4, 5, ...
d. 1, 4, 9, 16, ...

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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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Student Activity Sheet 1; Overview 1. REVIEW Look at the patterns below. Can you find the next two items in each list and state the rule for finding them? a. 2, 4, 6, 8, ... b. 2, 3, 5, 9, 17, ... c. 1, -2, 3, 4, 5, ...d. 1, 4, 9, 16, ...