Question

9. [-/1 Points) DETAILS LARPCALC10 10.6.052.MI. Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: x = h + r cosa, y = k + r sin a Need Help? Read it Watch It Master it Submit Answer

Answer 1

Given that,

x = h + r cos(α)

i.e. r cos(α) = x - h.......... (1)

And,

y = k + r sin(α)

i.e. r sin(α) = y - k.......... (2)

.

Now by squaring and adding, both the equations, we get,

r²​​​​​​cos²​​​​​​(α) + r²​​​​​​sin²​​​​​​(α) = (x - h)²​​​​​​ + (y - k)²​​​​​

i.e. r²​​​​​(cos²​​​​​​(α) + sin²​​​​​(α)) = (x - h)²​​​​​​ + (y - k)²

i.e. r²​​​​​​ = (x - h)²​​​​​​ + (y - k)²​​​​​

i.e. (x - h)²​​​​​​ + (y - k)²​​​​​​ = r²​​​​​

.

.

So the required rectangular equation is,

(x - h)²​​​​​​ + (y - k)²​​​​​​ = r²​​​​​​