Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2013MathematicsStraight Lines

The pair of lines 3 x^2-4 x y+ 3 y^2=0 are rotated about the origin by 6 in the anticlockwise sense. The equation of the pair in the new position is

Options

  1. Ax^2- 3 x y=0
  2. Bx y- 3 y^2=0
  3. C3 x^2-x y=0
  4. DNone of the above

Correct answer

C. 3 x^2-x y=0

Step-by-step solution

The given equation of pair of straight lines can be rewritten as ( 3 x-y)(x- 3 y)=0 . Their separate equations are, y= 3 x and y= 1 3 x y= 60^ x and y= 30^ x-y= 90^ x and y= 60^ x x=0 and y= 3 x Combined equation in the new position is x( 3 x-y)=0 or 3 x^2-x y=0

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

The locus of the third vertex of a right-angled triangle, the ends of whose hypotenuse are (1,2) and (4,5) , is 2025The coordinate axes are rotated about the origin in the counter clockwise direction through an angle 60^ . If a and b are the intercepts made on the new axes by a straight line who 2025The image of a point (2,-1) with respect to the line x-y+1=0 is 2025If a straight line is at a distance of 10 units from the origin and the perpendicular drawn from the origin to it makes an angle 4 with the negative X -axis in the negative directi 2025A straight line passing through the origin O meets the parallel lines 4 x+2 y=9 and 2 x + y +6=0 at the points P and Q respectively. Then the point O divides the line segment PQ in 2025A (4,3), B (2,5) are two points. If P is a variable point on the same side as that of the origin with respect to the line AB and is at most at a distance of 5 units from the midpoi 2025By shifting the origin to the point (2,3) through translation of axes, if the equation of the curve x^2+3 x y-2 y^2+4 x-y-20=0 is transformed to the form Ax ^2+ Bxy + Cy ^2+ Dx + E 2025The points (2,3) and (-4,- 4 3 ) lie on the opposite sides of the line L 5 x -6 y + k =0 and k is an integer. If the points (1,2) and (4,5) lie on the same side of the line L =0 , 2025 Full Straight Lines list All Manipal MET PYQs