By rearranging the equation of the conic, classify it as an ellipse,…


This distribute concerns the conic after a while equation
7x
2 + 12y
2 = 252.
(i) By rearranging the equation of the conic, adproper it as an ejection,
parabola or hyperbola in meaindisputable aspect, and paint the incurvation. [6]
(ii) Exhibition that the fair compute of the deviation can be written as
1
6
v
15 and future perceive fair computes of the foci and directrices. [5]
(iii) For each of the two points P where the conic intersects the x-axis,
and using the fair computes set in distribute (a)(ii) aloft, calculate
the distances P F and P d, where F is the rendezvous after a while negative
x-coordinate and d is the identical directrix, and exhibition that
P F = e Pd, where e is the deviation. (This affords a control to
your answers to distribute (a)(ii).) [4]
(b) Now weigh the incurvation after a while equation
7
4
x
2 - 7x + 3y
2 + 6y - 53 = 0.
(i) Exhibition that this incurvation is a conic which can be obtained from the
conic in distribute (a) by translation, and narrate the translation
required. [5]
(ii) Use your answers to distribute (a) to paint this conic, exhibitioning its
centre, vertices and axes of harmony, and the slopes of any
asymptotes. You should grant the fair coordinates of the points. [4]
(c) (i) Write down parametric equations for the conics in distributes (a)
and (b). [2]
In distribute (c)(ii) you should afford a printout exhibitioning your concoct.
(ii) Use the parametric equations in distribute (c)(i) to concoct twain conics on
the similar diagram, using Mathcad. (You may perceive it helpful to
start from Mathcad smooth 221A2-01.)
Document Preview:

Mathematics, Computing and Technology MS221 Exploring Mathematics MS221 Assignment Booklet I 2011B Contents Shave-off age 3 TMA MS221 01 (envelope Block A) 6 April 2011 7 TMA MS221 02 (envelope Block B) 15 June 2011 Instructions for succumbting assignments Delight cast all your answers to each savant-conspicuous assignment (TMA), conjointly after a while a completed assignment devise (PT3), to stretch your savant on or anteriorly the embezzle shave-off age exhibitionn aloft. Your savant accomplish indevise you environing the address to use for succumbting your TMAs. Delight don’t succumb your TMAs immediately to the University. Regrettably, the University is incompetent to recognize TMAs succumbted electronically on this module. If you tend any interrogations environing how best to fit and succumb your TMAs, delight apposition your savant. Be indisputable to grow in the rectify assignment calculate on the PT3 devise, and authorize suited season in the shaft for each assignment to stretch its use on or anteriorly the shave-off age. You are advised to tend a observation of your assignments in predicament of privation in the mail. Also tend all your conspicuous assignments as you may deficiency to shape intimation to them in following assignments or when you alter for the criterion. Copyright c! 2011 The Open University WEB 02082 8 15.1 Plagiarism The University weighs plagiarism to be a careful substance, and accordingly we describe your watchfulness to the postscript on plagiarism in the Tribute Handbook which is entitled ‘What constitutes plagiarism or trickery?’. Delight voice that intimations to ‘assignments’ should be enthralled to include any division of labor succumbted for tribute, not proper savant-conspicuous assignments. Points to voice when preparing solutions to TMA interrogations • Apposition your savant if the signification of any distribute of a interrogation does not look serene. • Your solutions should not envelop the use of Mathcad, bar in those distributes of interrogations where this is palpably required or suggested. • Where a interrogation envelops matter-of-fact regard, exhibition all your laboring. You may not accept unmeasured marks...

Attachments: