6.3 Parametric equations of curves (A-level only) Flashcards","topicId":"63abc86c-158b-4c15-b365-5bf878c0d853","topicSlug":"parametric-equations-of-curves","cards":[{"id":"422e68da-0f67-4a88-bc56-03000d7abb88","cardType":"basic","front":"

For a fixed value of $t$, how is a point on a parametric curve found?

","back":"

Substitute the same value of $t$ into both equations.

","points":1,"mcqOptions":null},{"id":"1750a477-c674-43e5-abcc-538d51031bb4","cardType":"basic","front":"

How is the direction of travel along a parametric curve determined?

","back":"

Follow the points as $t$ increases.

","points":1,"mcqOptions":null},{"id":"2f6f5476-fe0a-4a6f-bd87-f3c42dc47719","cardType":"basic","front":"

What effect does restricting the parameter interval have?

","back":"

It selects only the generated part of the Cartesian curve.

","points":1,"mcqOptions":null},{"id":"b1aba071-ca83-4135-9d5c-7daed5fec9a0","cardType":"basic","front":"

How are the endpoints of a curve with $a\\leq t\\leq b$ found?

","back":"

Substitute $t=a$ and $t=b$ into both equations.

","points":2,"mcqOptions":null},{"id":"de614d2b-441c-43fd-a68c-b2a7e94914e1","cardType":"basic","front":"

Find the endpoint when $t=-1$ for $x=t+1$, $y=t^2$.

","back":"

$(0,1)$

","points":1,"mcqOptions":null},{"id":"dd180f86-040b-4724-b985-a7ed2ee9030b","cardType":"basic","front":"

Find the endpoint when $t=2$ for $x=t+1$, $y=t^2$.

","back":"

$(3,4)$

","points":1,"mcqOptions":null},{"id":"b8c3bc4e-f518-4a0b-97e5-85694a863e89","cardType":"cloze","front":"

To eliminate a parameter, rearrange one equation for $t$ and [ ].

","back":"

To eliminate a parameter, rearrange one equation for $t$ and substitute it into the other equation.

","points":null,"mcqOptions":null},{"id":"2373b4c1-8cfb-4a46-a36b-d6efb6d7e86c","cardType":"basic","front":"

Make $t$ the subject of $x=3t-1$.

","back":"

$t=\\frac{x+1}{3}$

","points":1,"mcqOptions":null},{"id":"ab32a47c-644d-4ad9-835b-7cc14dd8241d","cardType":"cloze","front":"

If $t=\\frac{x+1}{3}$, then $t^2$ must be replaced by $\\text{[...]}$.

","back":"

If $t=\\frac{x+1}{3}$, then $t^2$ must be replaced by $\\boxed{\\left(\\frac{x+1}{3}\\right)^2}$.

","points":null,"mcqOptions":null},{"id":"3e07407a-dceb-484b-9fb0-2e527889ee61","cardType":"basic","front":"

Eliminate $t$ from $x=3t-1$, $y=2t^2+5$.

","back":"

$y=\\frac{2}{9}(x+1)^2+5$

","points":2,"mcqOptions":null},{"id":"bcaaeee6-224f-4cf3-9b07-a05ec40e4270","cardType":"basic","front":"

Eliminate $t$ from $x=2t+1$, $y=t^2-3$.

","back":"

$y=\\frac{(x-1)^2}{4}-3$

","points":2,"mcqOptions":null},{"id":"83d8d15e-ceef-434b-bf16-721900833774","cardType":"cloze","front":"

The identity used to eliminate $t$ from trigonometric parametrisations is $\\text{[...]}$.

","back":"

The identity used to eliminate $t$ from trigonometric parametrisations is $\\boxed{\\sin^2t+\\cos^2t=1}$.

","points":null,"mcqOptions":null},{"id":"9c6490f5-f980-430d-bab8-532abb88dd51","cardType":"basic","front":"

Eliminate $t$ from $x=a\\cos t$, $y=a\\sin t$.

","back":"

$x^2+y^2=a^2$

","points":2,"mcqOptions":null},{"id":"202fd886-6a88-4e55-9002-a2627e6a7a0b","cardType":"cloze","front":"

The standard parametrisation $x=a\\cos t$, $y=a\\sin t$ traces a circle of radius $\\text{[...]}$, provided $t$ covers a full revolution.

","back":"

The standard parametrisation $x=a\\cos t$, $y=a\\sin t$ traces a circle of radius $\\boxed{a}$, provided $t$ covers a full revolution.

","points":null,"mcqOptions":null},{"id":"727bbcbe-f81d-4362-8d0f-7e22d65e7344","cardType":"basic","front":"

Eliminate $t$ from $x=4\\cos t$, $y=3\\sin t$.

","back":"

$\\frac{x^2}{16}+\\frac{y^2}{9}=1$

","points":2,"mcqOptions":null},{"id":"8f

1.6.3 Parametric equations of curves (A-level only) Flashcards

1.6.3 Parametric equations of curves (A-level only) Flashcards