Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202628 January 2026Evening ShiftMathematicsCircleActual

Let the circle x²+y²=4 intersect x -axis at the points A ( a , 0), a >0 and B ( b , 0) . Let P (2 , 2 ) , 0< < 2 and Q (2 , 2 ) be two points such that ( - )= 2 . Then the point of intersection of AQ and BP lies on :

Options

  1. Ax²+y²-4 y-4=0
  2. Bx²+y²-4 x-4 y=0
  3. Cx²+y²-4 x-4=0
  4. Dx²+y²-4 x-4 y-4=0

Correct answer

A. x²+y²-4 y-4=0

Step-by-step solution

Let point of intersection R(h,k) m_ BR = m_ BP k h+2 = 2 2 + 2 k h+2 = 2 m_ AR = m_ AQ k h-2 = 2 2 - 2 = - 1 = - 2 2 - 2 = 4 ( 2 - 2 ) = 4 = 1 2 - 2 1 + 2 2 = 1 k h+2 + h-2 k 1 + ( k h+2 ) ( 2-h k ) = 1 k^2 + h^2 - 4 k(h+2) 4 h+2 = 1 h^2 + k^2 - 4 4k = 1 x^2 + y^2 - 4y - 4 = 0

Practice Circle on Quantrex Academy →

More from Circle

Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I List-II (P) The circle with centre (1, 2) and touching the straight line 3x + 4y = 2026Consider the circle C: x^2+y^2-6x-8y-11=0 . Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from th 2026Let C be a circle having centre in the first quadrant and touching the x -axis at a distance of 3 units from the origin. If the circle C has an intercept of length 6 3 on y -axis, 2026Let the line x - y = 4 intersect the circle C: (x-4)^2 + (y+3)^2 = 9 at the points Q and R . If P( , ) is a point on C such that PQ = PR , then (6 + 8 )^2 is equal to __________. 2026Let the centre of the circle x^2 + y^2 + 2gx + 2fy + 25 = 0 be in the first quadrant and lie on the line 2x - y = 4 . Let the area of an equilateral triangle inscribed in the circl 2026Let P be a moving point on the circle x^2 + y^2 - 6x - 8y + 21 = 0 . Then, the maximum distance of P from the vertex of the parabola x^2 + 6x + y + 13 = 0 is equal to: 2026Suppose that two chords, drawn from the point (1, 2) on the circle x^2 + y^2 + x - 3y = 0 are bisected by the y -axis. If the other ends of these chords are R and S , and the mid p 2026Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines x + (k-1)y + 3 = 0 and 2x + k^2 y - 4 = 0 . If the line x - y + 2026 Full Circle list All JEE Main PYQs