Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced2016MathematicsStraight LinesActual

Paragraph: Let F₁ (x₁, 0 ) and F₂ (x₂, 0 ) , for x₁ 0 , be the foci of the ellipse x² 9 + y² 8 =1 . Suppose a parabola having vertex at the origin and focus at F₂ intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. Question: The orthocentre of the triangle F₁ M N is

Options

  1. A- 9 10 ,   0
  2. B2 3 ,   0
  3. C9 10 ,   0
  4. D2 3 ,   6

Correct answer

A. - 9 10 ,   0

Step-by-step solution

x 2 9 + y 2 8 = 1 F 1 ( − 1 , 0 ) , F 2 ( 1 , 0 ) ⇒ Parabola is y 2 = 4 x The intersection of ellipse & parabola is M   &   N x 2 9 + 4 x 8 = 1 ⇒ M ( 3 2 , 6 )   &     N ( 3 2 , − 6 ) Equation of altitude through M   : y -   6 = 5 2 6   x - 3 2 Equation of altitude through F 1 : y = 0 Solving, we get orthocentre - 9 10 ,   0

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 JEE Advanced PYQs