Eliminate the parameter. x = 3t, y = t + 7

Solution:

Given, x = 3t ----------(1)

y = t + 7 -----------(2)

Now from (1)

t = x / 3, substitute in (2)

Then y = x/3 + 7

Multiply by 3 throughout,

3y = x + 21

∴ x - 3y + 21 = 0

Example: Eliminate the parameter ‘t’ in x = 4 cos t and y = 3 sin t

Given, x = 4 cos t and y = 3 sin t

⇒ cos t = x/4 and sin t = y/3

We have cos² t + sin² t = 1

⇒ (x/4)² + (y/3)² = 1

⇒ x²/16 + y²/9 = 1

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Eliminate the parameter. x = 3t, y = t + 7

Summary:

After eliminating the parameter in x = 3t, y = t + 7 we get x - 3y + 21 = 0