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

Answer:

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

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

Step-by-step 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 = $\sqrt{(7-10)^{2} + (4-0)^{2} }$

 = $\sqrt{(-3)^{2} + 4^{2} }$

 = $\sqrt{9 + 16}$

 = $\sqrt{25} = 5$

⇒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