MHT CET202620 April 2026Evening ShiftMathematicsStraight LinesActual
A straight line makes equal negative intercepts on the coordinate axes. If the perpendicular distance from the origin to the line is 4 units, then the equation of the line is ......
Options
- Ax + y + 4 = 0
- Bx + y + 4 2 = 0
- Cx - y + 4 = 0
- Dx - y + 4 2 = 0
Correct answer
B. x + y + 4 2 = 0
Step-by-step solution
Let the equation of the line in intercept form be x a + y b = 1 . Since the line makes equal negative intercepts on the coordinate axes, a = b = -c where c > 0 . The equation of the line becomes x -c + y -c = 1 x + y + c = 0 . The perpendicular distance from the origin (0,0) to this line is given as 4 units. Using the perpendicular distance formula, |0 + 0 + c| 1^2 + 1^2 = 4 . |c| 2 = 4 |c| = 4 2 . Since c > 0 , we have c = 4 2 . Substituting the value of c in the equation of the line, we get x + y + 4 2 = 0 . Answ