Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202611 April 2026Evening ShiftMathematicsThree Dimensional GeometryActual

If the lines x-1 2 = y+1 3 = z-1 4 and x-3 1 = y-c 2 = z 1 intersect, then the radius of circle x^2 + y^2 - 4x + 10y + c = 0 is

Options

  1. A9 2
  2. B9 2
  3. C7 2
  4. D7 2

Correct answer

C. 7 2

Step-by-step solution

The condition for the two lines to intersect is that they must be coplanar. vmatrix 3-1 & c-(-1) & 0-1 2 & 3 & 4 1 & 2 & 1 vmatrix = 0 vmatrix 2 & c+1 & -1 2 & 3 & 4 1 & 2 & 1 vmatrix = 0 Expanding the determinant along the first row: 2(3 - 8) - (c+1)(2 - 4) - 1(4 - 3) = 0 -10 + 2(c+1) - 1 = 0 2c - 9 = 0 c = 9 2 The equation of the circle is x^2 + y^2 - 4x + 10y + 9 2 = 0 . The radius of the circle is given by r = g^2 + f^2 - c . r = (-2)^2 + (5)^2 - 9 2 r = 4 + 25 - 9 2 r = 29 - 9 2 = 49 2 = 7 2 Answer: 7 2

Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

The circum radius of the triangle formed by the points (2,-1,1),(1,-3,-5) and (3,-4,-4) is 2025Let A (2,3,5), B (-1,3,2), C ( , 5, ) be the vertices of ABC . If the median through the vertex A is equally inclined to the coordinate axes, then 2025Equation of the plane passing through the origin and perpendicular to the planes x+2 y-z=1 and 3 x-4 y+z=5 is 2025If the line joining the points i +2 j and j -2 k intersects the plane passing through the points 2 i - j , 2 j +3 k and k -2 i at r , then r ( i + j + k )= 2025The vector equation of a plane passing through the line of intersection of the planes r ( i -2 k )=3, r (2 j + k )=5 and the point i +2 j +3 k is 2025The points A (-1,2,3), B (2,-3,1), C (3,1,-2) 2025The direction cosines of the line making angles 4 , 3 and (0 < < 2 ) respectively with X , Y and Z axes are 2025If the equation of the plane passing through the point (3,2,5) and perpendicular to the planes 2 x-3 y+5 z=7 and 5 x+2 y-3 z=11 is x+b y+c z+d=0 , then 2 b+3 c+d= 2025 Full Three Dimensional Geometry list All MHT CET PYQs