Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

Let two sides of a rectangle of area 20 sq. units are along lines x – y = 0 and x + y = 2 , then the locus of the point of intersection of diagonals is a

Options

  1. Apair of ellipse
  2. Bpair of straight lines
  3. Cpair of hyperbola having eccentricity 2 and 2 3
  4. Dpair of hyperbola each having eccentricity 2

Correct answer

D. pair of hyperbola each having eccentricity 2

Step-by-step solution

Let diagonals A C & B D intersect at F h , k ⇒ Area of quad D E F G is 1 4 20 = 5 Now distance of h , k from x + y = 2 and x – y = 0 is h + k - 2 2 & h - k 2 respectively. ⇒ h + k - 2 2 h - k 2 = 5 ⇒ ( h - 1 ) + ( k - 1 ) h - 1 - k - 1 = 10 ⇒ ( h - 1 ) 2 - ( k - 1 ) 2 = 10 ⇒ ( x - 1 ) 2 - ( y - 1 ) 2 = 10 or x - 1 2 - y - 1 2 = - 10 ⇒ Both are hyperbola with eccentricity = 2

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

If a straight line drawn through the point of intersection of the lines 4x+3y-1=0 and 3x+4y-1=0 , meets the co-ordinate axes at the points P and Q, then the locus of the mid point 2026From the point (-1, -1) , two rays are sent making angles of 45° with the line x + y = 0 . These rays get reflected from the mirror x + 2y = 1 . If the equations of the reflected r 2026In an equilateral triangle PQR , let the vertex P be at (3, 5) and the side QR be along the line x + y = 4 . If the orthocentre of the triangle PQR is ( , ) , then 9( + ) is equal 2026Let P(3 , 2 ) , 0 , be a point on the ellipse x^2 9 + y^2 4 =1 , Q be a point on the circle x^2+y^2-14x-14y+82=0 and R be a point on the line x+y=5 such that the centroid of the tr 2026Let A,B be points on the two half-lines x- 3 |y|= , >0 at a distance of from their point of intersection P . The line segment AB meets the angle bisector of the given half-lines at 2026Let the line L₁ : x + 3 = 0 intersect the lines L₂ : x - y = 0 and L₃ : 3x + y = 0 at the points A and B , respectively. Let the bisector of the obtuse angle between the lines L₂ a 2026Let the vertex A of a triangle ABC be (1, 2) , and the mid-point of the side AB be (5, -1) . If the centroid of this triangle is (3, 4) and its circumcenter is ( , ) , then 21( + ) 2026Let the mid points of the sides of a triangle ABC be ( 5 2 , 7 ) , ( 5 2 , 3 ) and (4, 5) . If its incentre is (h, k) , then 3h + k is equal to : 2026 Full Straight Lines list All NTA Abhyas JEE Main PYQs