Q.37 Which of the following curve/straight line equations will pass through the origin when
plotted on a graph?
(A) -x/2+y/2=0
(B)1+y+x=1
(C)xy=1
(D)2y-2x+2=0
Option (A) passes through the origin. A curve or line passes through the origin (0,0) if substituting x=0 and y=0 satisfies the equation. Testing each option reveals only (A) meets this condition.
Option Analysis
Substitute x=0, y=0 into each equation.
-
(A) -x/2 + y/2 = 0: Becomes 0=0, true. Rewrites as y=x, a line through origin.
-
(B) 1 + y + x = 1: Simplifies to x+y=0, but 0+0=0 ≠1, false.
-
(C) xy=1: 0*0=0 ≠1, false. This is a hyperbola not through origin.
-
(D) 2y – 2x + 2 = 0: -2x + 2y = -2, but 0+0=0 ≠-2, false. Rewrites as y=x-1, y-intercept -1.
The equation passes through origin when (0,0) satisfies it, vital for graphing lines like y=mx (no intercept). This MCQ tests coordinate geometry basics for exams like CSIR NET.
Graph Insights
Lines through origin follow y=mx or ax+by=0. Option A simplifies to y=x, slope 1, passing (0,0). Others shift away: B parallel to y=-x but offset, C asymptotic to axes, D intercepts at (0,-1).
