Convert to a rectangular equation by eliminating the parameter:
x=(1/t) y=2t+3
from x = 1/t ---> t = 1/x
from y = 2t+3 ---> t = (y-3)/2
1/x = (y-3)/2
xy - 3y = 2
To convert the given parametric equations to a rectangular equation, we need to eliminate the parameter (t) and express x and y directly in terms of each other.
We start with the given equations:
x = 1/t
y = 2t + 3
To eliminate t, we can solve the first equation for t in terms of x:
x = 1/t
Cross-multiplying, we get:
xt = 1
Solving for t:
t = 1/x
Now, substitute this expression for t in the second equation:
y = 2t + 3
y = 2(1/x) + 3
To simplify further, we need to find a common denominator for the fraction:
y = 2/x + 3
To combine the terms, we need a common denominator of x:
y = 2/x + (3x/x)
y = (2 + 3x)/x
Therefore, the rectangular equation is:
y = (2 + 3x)/x