Doubts
Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents
Sign in to save progress →
Doubts
Sign in

Straight Lines and Pair of Straight Lines question

2025 · 22 Jan · Shift 2 · Q49
Guest · try one question or challengeGuest · try one question or challenge
  1. PYQ Library
  2. /JEE Main
  3. /Mathematics
  4. /Straight Lines and Pair of Straight Lines
  5. /2025 · 22 Jan · Shift 2 · Q49

Straight Lines and Pair of Straight Lines question

2025 · 22 Jan · Shift 2 · Q49

JEE MainMathematicsStraight Lines and Pair of Straight LinesNumerical+4 / −1
Let the distance between two parallel lines be 5 units and a point PPP lie between the lines at a unit distance from one of them. An equilateral triangle PQRP Q RPQR is formed such that QQQ lies on one of the parallel lines, while R lies on the other. Then (QR)2(Q R)^2(QR)2 is equal to ‾\underline{\hspace{2cm}}​.
Numerical answer
PreviousNext

More from Straight Lines and Pair of Straight Lines

  • A rod of length eight units moves such that its ends A and B always lie on the lines x−y+2=0 and y+2=0, respectively. If the locus of the point P, that divides the rod AB internally in the ratio 2:1 is 9(x2+αy2+βxy+γx+28y)−76=0…2025 · MCQ
  • Let the lines 3x−4y−α=0,8x−11y−33=0, and 2x−3y+λ=0 be concurrent. If the image of the point (1,2) in the line 2x−3y+λ=0 is (1357​,13−40​), then ∣αλ∣ is equal to2025 · MCQ
  • Let the points (211​,α) lie on or inside the triangle with sides x+y=11,x+2y=16 and 2x+3y=29. Then the product of the smallest and the largest values of α is equal to :2025 · MCQ
  • Two equal sides of an isosceles triangle are along −x+2y=4 and x+y=4. If m is the slope of its third side, then the sum, of all possible distinct values of m, is:2025 · MCQ
  • If A and B are the points of intersection of the circle x2+y2−8x=0 and the hyperbola 9x2​−4y2​=1 and a point P moves on the line 2x−3y+4=0, then the centroid of ΔPAB lies on the line :2025 · MCQ
  • Let ΔABC be a triangle formed by the lines 7x – 6y + 3 = 0, x + 2y – 31 = 0 and 9x – 2y – 19 = 0. Let the point (h, k) be the image of the centroid of ΔABC in the line 3x + 6y – 53 = 0. Then h2 + k2 + hk is equal to :2025 · MCQ
  • Let the line x + y = 1 meet the axes of x and y at A and B, respectively. A right angled triangle AMN is inscribed in the triangle OAB, where O is the origin and the points M and N lie on the lines OB and AB, respectively. If the area of…2025 · MCQ
  • Let ABC be an isosceles triangle in which A is at (−1,0),∠A=32π​,AB=AC and B is on the positve x-axis. If BC=43​ and the line BC intersects the line y=x+3 at $(\alpha,…2024 · Numerical