Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Find the Point to Which the Origin Should Be Shifted After a Translation of Axes So that the Following Equation Will Have No First Degree Terms: X2 − 12x + 4 = 0 - Mathematics

Sum

Find the point to which the origin should be shifted after a translation of axes so that the following equation will have no first degree terms: x2 − 12x + 4 = 0

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Solution

Let the origin be shifted to (h, k). Then, x = X + h and y = Y + k.
Substituting x = X + h and y = Y + k in the equation x2 − 12x + 4 = 0, we get:
\[\left( X + h \right)^2 - 12\left( X + h \right) + 4 = 0\]
\[ \Rightarrow X^2 + 2hX + h^2 - 12X - 12h + 4 = 0\]
\[ \Rightarrow X^2 + X\left( 2h - 12 \right) + h^2 - 12h + 4 = 0\]
For this equation to be free from the terms containing X and Y, we must have

\[2h - 12 \Rightarrow h = 6\]
Hence, the origin should be shifted to the point \[\left( 6, k \right), k \in R\].
Concept: Brief Review of Cartesian System of Rectanglar Co-ordinates
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 22 Brief review of cartesian system of rectangular co-ordinates
Exercise 22.3 | Q 7.3 | Page 21
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