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

Parabola question

2021 · Shift 2 · Q25
Guest · try one question or challengeGuest · try one question or challenge
  1. PYQ Library
  2. /JEE Advanced
  3. /Mathematics
  4. /Parabola
  5. /2021 · Shift 2 · Q25

Parabola question

2021 · Shift 2 · Q25

JEE AdvancedMathematicsParabolaMultiple correct+4 / −2
Let E denote the parabola y2 = 8x. Let P = (−-− 2, 4), and let Q and Q' be two distinct points on E such that the lines PQ and PQ' are tangents to E. Let F be the focus of E. Then which of the following statements is(are) TRUE?
  1. A
    The triangle PFQ is a right-angled triangle
  2. B
    The triangle QPQ' is a right-angled triangle
  3. C
    The distance between P and F is 5 2\sqrt 22​
  4. D
    F lies on the line joining Q and Q'
PreviousNext

More from Parabola

  • Let a, b and λ be positive real numbers. Suppose P is an end point of the latus return of the parabola y2 = 4 λ x, and suppose the ellipse a2x2​+b2y2​=1 passes through the point…2020 · MCQ
  • Let the circles C1 : x2 + y2 = 9 and C2 : (x − 3)2 + (y − 4)2 = 16, intersect at the points X and Y. Suppose that another circle C3 : (x − h)2 + (y − k)2 = r2 satisfies the following conditions : (i) Centre of C3 is collinear with… Includes diagram2019 · MCQ
  • Let the circle C1 : x2 + y2 = 9 and C2 : (x − 3)2 + (y − 4)2 = 16, intersect at the points X and Y. Suppose that another circle C3 : (x − h)2 + (y − k)2 = r2 satisfies the following conditions : (i) centre of C3 is collinear with… Includes diagram2019 · MCQ
  • If a chord, which is not a tangent, of the parabola y2 = 16x has the equation 2x + y = p, and mid-point (h, k), then which of the following is(are) possible value(s) of p, h and k?2017 · Multiple correct
  • By appropriately matching the information given in the three columns of the following table. Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively. If a tangent to a suitable conic… Includes table2017 · MCQ
  • The circle C1​:x2+y2=3, with centre at O, intersects the parabola x2=2y at the point P in the first quadrant, Let the tangent to the circle C1​, at P touches other two circles C2​ and C3​ at R2​…2016 · Multiple correct
  • Let P be the point on the parabola y2=4x which is at the shortest distance from the center S of the circle x2+y2−4x−16y+64=0. Let Q be the point on the circle dividing the line segment SP internally. Then2016 · Multiple correct
  • Let P and Q be distinct points on the parabola y2=2x such that a circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle ΔOPQ is 32​,…2015 · Multiple correct