﻿ Determiner as to what point the axes of the coordinates be shifted so as to remove the first degree terms from the equation            f (x, y) = 2x2 + 3y2 – 12x + 12y + 24 = 0 : Kaysons Education

# Determiner As To What Point The Axes Of The Coordinates Be Shifted So As To Remove The First Degree Terms From The Equation            f (x, Y) = 2x2 + 3y2 – 12x + 12y + 24 = 0

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## Question

### Solution

Correct option is

(3, –2)

Let the origin be shifted to (h, k).

Old New Pt.

x = X + h

y = Y + k

2(X + h)2 + 3(Y + k)2 – 12(X +h) + 12 (Y + k) + 24 = 0

2X2 + 3Y2 + X(2h – 12) + Y(6k + 12) + (12h2 + 3k2 – 12h + 12k) = 0

Since the equation is to be free of first degree terms, therefore coefficients of X and Y is each separately zero.

∴ 4h – 12 = 0 and 6k + 12 = 0

∴    (h, k) = (3, –2)

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