Question

The positive solutions of the equation \[ax + by + c = 0\] always lie in the
A) 1st quadrant
B) 2nd quadrant
C) 3rd quadrant
D) 4th quadrant

Answer 1

Hint: The nature of solution will decide the placing of point in quadrant. Here variable will give the value of \[x{\rm{ }}coordinate{\rm{ }}and{\rm{ }}y\] will be for \[y{\rm{ }}coordinate\] .

Complete step-by-step solution:
Given: If \[ax + by + c = 0\] has a positive solution, then which quadrant contains its point for all values.
>Option A 1st quadrant: As the coordinates of all the points in 1st quadrant is positive. Though if a line passes through 1st then all the solution points lying on the line in 1st quadrant must be positive. Therefore, this option is correct.
>Option B 2nd quadrant: As the \[x\;coordinates\] in this quadrant is negative. Though if a line passes through the 2nd quadrant then all the solution points lying on the line must not be positive. Therefore, this option is incorrect.
>Option C 3rd quadrant: As \[x{\rm{ }}and{\rm{ }}y{\rm{ }}coordinates\] in this quadrant is negative. Though if a line passes through the 3rd quadrant then all the solution points lying on the line will be negative. Therefore, this option is incorrect.
>Option D 4th quadrant: As \[y{\rm{ }}coordinate\] is negative in the 4th quadrant. Though if a line passes through the 4th quadrant then all the solution points on the line must not be positive. Therefore, this option is incorrect.

 Hence, Option A is only correct.

Note:In such types of questions we need to focus on what type of data is being needed to place in the quadrants like here the data is all positive solutions. As all points should be positive so only the first quadrant contains points that must be positive. Here it always means for all values of x and y from the equation.