« MATHS 1B
1
BABY BULLET-Q «
2. TRANSFORMATION OF AXES
1 X 4 = 4 Marks
@IMP FORMULAS, KEY CONCEPTS?
I) TRANSLATION OF AXES (shifting of origin):
1.1) To find (i) Transformed (new) equation (ii) Old coordinates of a given point,
use the relations x = X + h, y = Y + k
1.2) To find the (i) original equation (ii) new coordinates, use the relations X = x - h, Y = y - k
- Q
2.1) The point to which the origin should be shifted to eliminate the first degree terms
T
(i.e., x term & y term) in the equation ax 2 2hxy by 2 2gx 2fy c 0 is
§ hf bg gh af ·
¨ 2
,
2¸
© ab h ab h ¹
,ab z h 2
L E
L
U
2.2) The point to which the axes be translated to eliminate x,y terms in the equation
ax2 + by2 + 2gx + 2fy + c = 0 is (-g/a, -f/b)
B
2.3) The point to which the axes be translated to eliminate x,y terms in 2hxy + 2gx + 2fy + c = 0
is (-f/h, -g/h)
Y
B
2.4) The point to which the axes be translated to eliminate x, y terms in (x - a)2 + (y - b)2 = k is
(a, b) A
II. ROTATION OF AXES:
B X Y
1) The formulae in the rotation of axes are given in the tabular form: x cosq -sinq
y sinq cosq
1.1) To find (i) Transformed (new) equation (ii) old coordinates of a given point,
use the relations x = Xcosq - Ysinq; y = Ycosq + Xsinq
1.2) To find (i) the original equation (ii) the new coordinates of a given point,
use the relations X = xcosq + ysinq; Y = ycosq - xsinq
2) In order to eliminate the xy term in ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 the axes should be
1 § 2h ·
rotated through an angle T Tan 1 ¨ ¸
2 ©ab¹
