Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20248 Apr 2024Evening ShiftMathematicsStraight LinesActual

If the image of the point (-4,5) in the line x+2 y=2 lies on the circle (x+4)^2+(y-3)^2=r^2 , then r is equal to:

Options

  1. A2
  2. B3
  3. C1
  4. D4

Correct answer

A. 2

Step-by-step solution

Image of point (-4,5) x-x₁ a = y-y₁ b =-2 ( a x₁+b y₁+c a^2+b^2 ) Line: x+2 y-2=0 x+4 1 = y-5 2 =-2 ( -4+10-2 1^2+2^2 )= -8 5 x=-4- 8 5 =- 28 5 y=- 16 5 +5= 9 5 Point lies on circle (x+4)^2+(y-3)^2=r^2 aligned & 64 25 + ( 9 5 -3 )^2=r^2 & 100 25 =r^2, r=2 aligned

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 Main PYQs