Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201822 Apr 2018Evening ShiftMathematicsStraight LinesActual

If the straight line L 3 x+4 y-k=0 cuts the line segment joining the points P(2,-1) and Q(1,1) in the ratio 4: 1 , then the equation of the line parallel to the line y=x and concurrent with the lines P Q and L=0 is

Options

  1. A2 x-2 y+7=0
  2. Bx-y+1=0
  3. C5 x-5 y-3=0
  4. Dy=x+3

Correct answer

C. 5 x-5 y-3=0

Step-by-step solution

Point of intersection of given line L=0 and line segment P Q is R ( (4 1)+(1 2) 5 , (4 (1))+(1 (-1)) 5 )=R ( 6 5 , 3 5 ) Now, point R on the Line L=0 , So, 18 5 + 12 5 -k=0 k=6 Now, equation of Line concurrent with the lines L=0 and P Q is Line Eq. (i) is parallel to the Line y=x , so aligned - 3+2 4+ & =1 & =- 7 3 . aligned Equation of required line is 5 x-5 y-3=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 AP EAMCET PYQs