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Question 4 (Unit C4)20 marks Apply Strategy C25 in Unit C4 to write the quadric with equation in standard form Which of the six types of quadric does this represent?
U, 1U Identify a given quadric from its equation, we will the axes and translate the origin to obtain an equation that resemble equation of a quadric in standard position: we say that such an equat a quadric is in standard form. So, for example, the equation is an equation of a hyperboloid of one sheet in standard form, although is not in standard position. To write the equation of a quadric in standard form, we use the same techniques that we used for conics: introducing matrices, orthogonal diagonalisation and completing the square. We omit the justification -it analogous to that for conics. We summarise this method in the following strategy Strategy C25 To write the quadric with equation in standard form, do the following. 1. Introduce matrices: write down the matrices
2. Align the axes: orthogonally diagonalise A to get dz00) find (f h)-JTP, and write the quadric in the form g 3. Translate the origin: complete the squares mak e a substitution to change to the coordinate system exercise and exercises illustrate this strategy orked Exercise C75 e Strategy C25 to of 322 ite the quadric with equation it gh t of the six types of quadric does this repr it is with cont on
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