Edexcel A Level Maths: Pure:復習筆記9.1.2 Parametric Equations - Eliminating the Parameter
Parametric Equations - Eliminating the Parameter
What does eliminating the parameter mean??
- In parametric equations,?x = f(t)?and?y = g(t)
- There is still a connection directly linking?x?and?y
- This will be the?Cartesian?equation of the graph
How do I find the Cartesian equation from parametric equations??
- STEP 1: Rearrange one of the equations to make t the subject
- Either?t = p(x)?or?t = q(y)
- STEP 2: Substitute into the other equation
- STEP 3 Rearrange into the desired (Cartesian) form
How do I eliminate t when trig is involved?
- STEP 1? Rearrange both equations into the forms “cos t = …” and “sin t = …”
- STEP 2? Square BOTH sides of BOTH equations
- STEP 3? Add the equations together
- STEP 4? The trig identity “
” eliminates?t - STEP 5? Rearrange into desired (Cartesian) form
- This technique is seen in Trigonometric Identities
Exam Tip
When choosing which equation to rearrange, aim for “as simple as possible”:
- Linear equations are simpler than quadratics
- eg Rearrange?x = 2t + 3or
y = 3t2?+3t -4??
- eg Rearrange?x = 2t + 3or
- Single exponential terms are quite easy to deal with
- eg?x = e
?→?t = ln x
- eg?x = e
Trig identities may be needed and remember?squared?terms are good!
- eg?sin2 x + cos2?x?≡?1
Worked Example
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