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TEA [102]
3 years ago
10

What is the radius of a circle whose equation is X^2 plus Y^2 -10X +6 X +18=0?

Mathematics
1 answer:
frosja888 [35]3 years ago
3 0

ANSWER

The radius is 4

EXPLANATION

The given equation is:

{x}^{2}  +  {y}^{2}  - 10y + 6x + 18 = 0

We complete the square to get the expression in standard form:

{x}^{2}  + 6x +  {y}^{2}  - 10y  + 18 = 0

{x}^{2}  + 6x +  9 + {y}^{2}  - 10y  + 25  =  - 18 + 9 + 25

We factor using perfect squares to get:

{(x + 3)}^{2}  +  {(y - 5)}^{2} =  16

This implies that,

{(x + 3)}^{2}  +  {(y - 5)}^{2} =   {4}^{2}

Comparing to

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

The radius is r=4

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Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

The multiplication of whole numbers may be thought as a repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the value of the other one, the multiplier. The multiplier can be written first and multiplicand second (though the custom can vary by culture[1]).

{\displaystyle a\times b=\underbrace {b+\cdots +b} _{a}} a\times b=\underbrace {b+\cdots +b} _{a}

For example, 4 multiplied by 3 (often written as {\displaystyle 3\times 4} 3\times 4 and spoken as "3 times 4") can be calculated by adding 3 copies of 4 together:

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Here 3 and 4 are the factors and 12 is the product.

One of the main properties of multiplication is the commutative property: adding 3 copies of 4 gives the same result as adding 4 copies of 3:

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To know more about variance click the link given below.

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