Question

The CB radio of a trucker covers the circular area of (7,4). Find the equation of that circle. Give your answer in both standard and general form.

Answer 1

Standard form is - (x - 7)² + (y - 4)² = 5²

General form is - x² + y² - 14x - 8y + 40 = 0

Explanation:

Given - The CB radio of a trucker covers the circular area of (7,4).

Find the equation of that circle.

To find - Find the equation of that circle. Give your answer in both

standard and general form.

Proof -

Given that,

Center of CB radio = (7, 4)

Point on the Boundary = (10, 0)

Now,

We know that radius, r is

r =
`\sqrt{(7-10)^(2) + (4-0)^(2) }`

=
`\sqrt{(-3)^(2) + 4^(2) }`

=
`√(9 + 16)`

=
`√(25) = 5`

⇒r = 5

∴ we get

Standard form is - (x - 7)² + (y - 4)² = 5²

General form is -

x² + 7² - 2·7·x + y² + 4² - 2·4·y = 25

⇒x² + 49 - 14x + y² + 16 - 8y = 25

⇒x² + 65 - 14x + y² - 8y = 25

⇒x² + 65 - 14x + y² - 8y - 25 = 0

⇒x² - 14x + y² - 8y + 40 = 0

So, the general form is -

x² + y² - 14x - 8y + 40 = 0