731200c16","title":"3.2.1 Co-ordinate geometry in the (x, y) plane (A-level only) Flashcards","topicId":"18da69f2-203c-41a0-910a-0a32ff887d02","topicSlug":"co-ordinate-geometry-in-the-x-y-plane-10","cards":[{"id":"7f8e8f62-4eca-449b-ad27-6c341475035d","cardType":"basic","front":"Why can the circle $x^2+y^2=25$ not be written as one equation $y=f(x)$?","back":"Most $x$-values correspond to two $y$-values.","points":2,"mcqOptions":null},{"id":"43b3be7b-6d5b-4d28-b6fe-23cb3834c4d4","cardType":"cloze","front":"Parametric equations express $x$ and $y$ separately as functions of a [ ].","back":"Parametric equations express $x$ and $y$ separately as functions of a parameter.","points":null,"mcqOptions":null},{"id":"4525a6cb-f871-4b48-8147-9d616a050339","cardType":"cloze","front":"The amount of a parametric curve traced is determined by the [ ].","back":"The amount of a parametric curve traced is determined by the allowed parameter range.","points":null,"mcqOptions":null},{"id":"c067f379-3e7f-4923-af2f-f78f6faee0c9","cardType":"cloze","front":"The [ ] of a parametric curve is its direction as the parameter increases.","back":"The orientation of a parametric curve is its direction as the parameter increases.","points":null,"mcqOptions":null},{"id":"e42f9493-af72-40cb-9ead-99b6f1f37b53","cardType":"basic","front":"For $x=2t-1$ and $y=t^2+3$, what point corresponds to $t=-1$?","back":"The point is $(-3,4)$.","points":1,"mcqOptions":null},{"id":"eb706654-777c-41bc-9588-b161afdae5de","cardType":"basic","front":"For $x=t$, what restriction on $x$ follows from $-1\\le t\\le2$?","back":"$-1\\le x\\le2$.","points":1,"mcqOptions":null},{"id":"5261c24e-b4a4-48a7-9f9b-a977a87d3ddb","cardType":"cloze","front":"Eliminating the parameter produces an equation containing only [ ].","back":"Eliminating the parameter produces an equation containing only $x$ and $y$.","points":null,"mcqOptions":null},{"id":"1f589d03-7d56-4f8e-a97e-0532d049b2bb","cardType":"basic","front":"Make $t$ the subject of $x=3t+1$.","back":"$t=\\frac{x-1}{3}$.","points":1,"mcqOptions":null},{"id":"331de02b-85ea-4236-a30e-3bed2d9cc58b","cardType":"basic","front":"Eliminate $t$ from $x=3t+1$ and $y=2t^2$.","back":"$y=\\frac{2}{9}(x-1)^2$.","points":2,"mcqOptions":null},{"id":"e15bc552-7fb5-43ad-ade2-7647d7387252","cardType":"basic","front":"What restriction follows from $x=t^2+1$?","back":"$x\\ge1$, since $t^2\\ge0$.","points":2,"mcqOptions":null},{"id":"1a176297-e37a-4625-8e59-03c9da74713a","cardType":"basic","front":"Eliminate $t$ from $x=t^2+1$ and $y=3t^2-4$.","back":"$y=3x-7$, with $x\\ge1$.","points":2,"mcqOptions":null},{"id":"26da4959-841f-4f9c-a868-14ddc6d77593","cardType":"cloze","front":"Trigonometric parameters are eliminated using $\\text{[...]}$.","back":"Trigonometric parameters are eliminated using $\\boxed{\\sin^2\\theta+\\cos^2\\theta=1}$.","points":null,"mcqOptions":null},{"id":"e02acb4e-61b5-4b95-af88-2449a243eb23","cardType":"basic","front":"Convert $x=4\\cos\\theta$, $y=3\\sin\\theta$ to Cartesian form.","back":"$\\frac{x^2}{16}+\\frac{y^2}{9}=1$.","points":2,"mcqOptions":null},{"id":"835065f5-a939-4f65-93f5-2314413aedd4","cardType":"basic","front":"If $x=4\\cos\\theta$, what is $\\cos^2\\theta$ in terms of $x$?","back":"$\\cos^2\\theta=\\frac{x^2}{16}$.","points":1,"mcqOptions":null},{"id":"e0dc4551-d706-409c-9cc8-43ade74ea884","cardType":"basic","front":"Where does $x=r\\cos\\theta$, $y=r\\sin\\theta$ start when $\\theta=0$?","back":"It starts at $(r,0)$.