Respuesta :
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 = [tex]\sqrt{(7-10)^{2} + (4-0)^{2} }[/tex]
= [tex]\sqrt{(-3)^{2} + 4^{2} }[/tex]
= [tex]\sqrt{9 + 16}[/tex]
= [tex]\sqrt{25} = 5[/tex]
⇒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
