Question

Axes are rotating through a +ive obtuse angle θ so that the transformed equation of the curve 3x2 – 6xy + 3y2 + 7– 3 = 0 is free from the term of xy then the coefficient of x2 in the transformed equation is…

Solution

Correct option is

6

 

     

Coefficient of xy = 0

  

  

Since θ is obtain we choose 

  Coefficient of x2

     

     

SIMILAR QUESTIONS

Q1

A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 is

Q2

Let P = (–1, 0), Q = (0, 0) and  be three points. Then the equation of the bisector of the angle PQR is

Q3

Area of Δ formed by line x + y = 3 and  bisectors of pair of straight lines x2 – y2 +2y = 1is

Q4

The equation of the straight line which passes through the point (1, –2) and cuts off equal intercepts from the axes will be

Q5

The three lines 3x + 4y + 6 = 0,  and 4x + 7y + 8 = 0 are

Q6

The line (p + 2q)x + (p – 3q)y = p – q for different values of p and qpasses through the point

Q7

The locus of the mid-point of te portion intercepted between the axes by the line  where is constant is

Q8

The straight line passing through the point of intersection of the straight lines x – 3y + 1 = 0 and 2x + 5y – 9 = 0 and having infinite slope and at a distance 2 unit from the origin has the equation

Q9

shifting of origin (0, 0) to (h, k)

                        

                  Rotation of axes through an angle θ.

                          

1:- by rotating the axes through an angle θ the equation xy – y2 – 3+ 4 = 0 is transformed to the from which does not contain the term of xy then  ….

Q10

 A1(x1, y1), A2(x2y2), A3(x3y3), …. are n points in a plane such that

1:- A1 A2 is at G1G2A3 is divided in the ratio 1 : 2 at G2G3A4 is divided in the ratio 1 : 3 at G3. The process is continued unit all n points are exhausted, then find the coordinates of the final point Gn