CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The point to which the axes are to be translated to eliminate x and y terms in the equation 3x2−4xy−2y2−3x−2y−1=0 is

A
(52,3)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
(4,32)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(2,3)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(2,3)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A (52,3)
Given equation is 3x24xy2y23x2y1=0

Let (x1,y1) be a point to which the origin is shifted by translation

Let (X,Y) be the new coordinates of the point (x,y)

the equations of the transformation are x=X+x1,y=Y+y1

Now the transformed equation is
3(X+x1)24(X+x1)(Y+y1)2(Y+y1)23(X+x1)2(Y+y1)1=0

3(X2+2Xx1+x12)4(XY+Xy1+Yx1+x1y1)2(Y2+y12+2YY1)3Xx12Y2y11=0

3X2+3x12+6Xx14Xy14x1Y4x1y12Y22y12+4Yy13X3x12Y2y11=0

(3X24XY2Y2)+(3x122y124x1y13x12y11)+2X(3x12y132)+2Y(2x1+2y11)=0

Solving the first degree terms,we have
3x12y1=32

2x1+2y1=1

Adding the above equations, we get
3x12y12x1+2y1=32+1

x1=52

From equation ,2x1+2y1=1

2y1=1+2x1=1+2×52=1+5=6

y1=62=3

(x1,y1)=(52,3)

Hence the point is (52,3)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Hyperbola and Terminologies
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon