Question

1. Rewrite the following equations in the form (x−a)^2+(y−????)^2=????^2.

a. x^2+4x+4+y^2−6x+9=36
b. x^2−10x+25+y^2+14y+49=4

Answer 1

(a)
`(x+2)^2+(y-3)^2=6^2`

(b)
`(x-5)^2+(y+7)^2=2^2`

Explanation:

The standard form of circle is

`(x-a)^2+(y-b)^2=r^2`

where, (a,b) is center and r is radius.

Properties of algebra:

`(a+b)^2=a^2+2ab+b^2`

`(a-b)^2=a^2-2ab+b^2`

(a)

Consider the given equation is

`x^2+4x+4+y^2-6y+9=36`

`(x^2+4x+4)+(y^2-6y+9)=36`

`(x^2+2x(2)+2^2)+(y^2-2y(3)+3^3)=6^2`

Using properties of algebra, we get

`(x+2)^2+(y-3)^2=6^2`

(b)

Consider the given equation is

`x^2-10x+25+y^2+14y+49=4`

`(x^2-10x+25)+(y^2+14y+49)=4`

`(x^2-2x(5)+5^2)+(y^2+2y(7)+7^2)=2^2`

Using properties of algebra, we get

`(x-5)^2+(y+7)^2=2^2`