Respuesta :
The parametric equations for the line passes through the points (X₁ , Y₁) and (X₂ , Y₂) are :
X = X₁ + t (X₂ - X₁) ......................... (1)
Y = Y₁ + t (Y₂ - Y₁) .......................... (2)
For eliminating the parameter (t) , first we will solve any one equation for 't' and then substitute that into another equation.
From the equation (1),
⇒ t = [tex] \frac{X- X1}{(X2 - X1)} [/tex]
Substituting this t = [tex] \frac{X- X1}{(X2 - X1)} [/tex] into the equation (2), we will get :
Y = Y₁ + [tex] \frac{(X- X1)}{(X2 - X1)} [/tex] (Y₂ - Y₁)
Y = Y₁ + [tex] \frac{(X- X1)(Y2 - Y1)}{(X2 - X1)} [/tex]
So, this is the standard form of rectangular equation.
For two given points (0, 0) and (4, -4)
X₁ = 0 , Y₁ = 0, X₂ = 4 and Y₂ = -4
For finding the parametric equations, we will plug these values into the given parametric equations.
X = X₁ + t (X₂ - X₁)
⇒ X = 0+ t (4 - 0)
⇒ X = 4t
and Y = Y₁ + t (Y₂ - Y₁)
⇒ Y = 0+ t (-4 - 0)
⇒ Y = - 4t
So, the parametric equations for the line passing through (0,0) and (4, -4) are: X = 4t and Y = -4t
