Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Find What the Following Equation Become When the Origin is Shifted to the Point (1, 1). X2 − Y2 − 2x + 2y = 0 - Mathematics

Sum

Find what the following equation become when the origin is shifted to the point (1, 1).
x2 − y2 − 2x + 2y = 0

#### Solution

The given equation is x2 − y2 − 2x + 2y = 0.
Substituting $x = X + 1, y = Y + 1$ in the given equation, we get:
$\left( X + 1 \right)^2 - \left( Y + 1 \right)^2 - 2\left( X + 1 \right) + 2\left( Y + 1 \right) = 0$
$\Rightarrow X^2 + 2X + 1 - Y^2 - 2Y - 1 - 2X - 2 + 2Y + 2 = 0$
$\Rightarrow X^2 - Y^2 = 0$
Hence, the transformed equation is $x^2 - y^2 = 0$

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 6.4 | Page 21