Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202524 Jan 2025Morning ShiftMathematicsCircleActual

Let circle C be the image of x^2+y^2-2 x+4 y-4=0 in the line 2 x-3 y+5=0 and A be the point on C such that O A is parallel to x -axis and A lies on the right hand side of the centre O of C . If B( , ) , with 4 , lies on C such that the length of the are A B is (1 / 6)^ th of the perimeter of C , then - 3 is equal to

Options

  1. A3+ 3
  2. B4
  3. C4- 3
  4. D3

Correct answer

B. 4

Step-by-step solution

Centre (1,-2), r=3 Reflection of (1,-2) about 2 x-3 y+5=0 aligned & x-1 2 = y+2 -3 = -2(2+6+5) 13 =-2 & x=-3, y=4 aligned Equation of circle ' C ' C:(x+3)^2+(y-4)^2=9 A.T.Q. aligned & ( arcAB )= 1 6 2 r & r = 1 6 2 r & = 3 & ( +6)^2+( -4)^2=27 & ( +3)^2 ( -4)^2=9 ( +6)^2-( +3)^2=18 & 6 =-9 aligned aligned & = -3 2 , = (4- 3 3 2 ) & - 3 & (4- 3 3 2 )+ 3 3 2 & =4 aligned

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