Pls help..Write the standard form of the equation 2)옮리18112925225(x +(у +=12

Given the equation, 125x2-1825x+19y2+89y+1129225=1 To determine the standard form of the equation.…

Answered: 1129 225 (х+ (у + =1 12

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Pls help.. Write the standard form of the equation

Expert Solution

Step 1

Given the equation,

$\frac{1}{25} x^{2} - \frac{18}{25} x + \frac{1}{9} y^{2} + \frac{8}{9} y + \frac{1129}{225} = 1$

To determine the standard form of the equation.

$\begin{array}{rcl} \frac{1}{25} (x^{2} - 18 x) + \frac{1}{9} (y^{2} + 8 y) + \frac{1129}{225} & = & 1 \\ \frac{1}{25} (x^{2} - 18 x + 81 - 81) + \frac{1}{9} (y^{2} + 8 y + 16 - 16) + \frac{1129}{225} & = & 1 \\ \frac{1}{25} {(x - 9)}^{2} - \frac{81}{25} + \frac{1}{9} {(y + 4)}^{2} - \frac{16}{9} + \frac{1129}{225} & = & 1 \\ \frac{1}{25} {(x - 9)}^{2} + \frac{1}{9} {(y + 4)}^{2} & = & 1 \end{array}$

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