jee question practice
Answers
Topic :
Coordinate Geometry
Given :
There is a point on the straight line, 3x + 5y = 15 which is equidistant from coordinate axes.
To Find :
The possible quadrant in which given point can lie.
Solution :
If the given point is equidistant from coordinate axes then it must lie on |x| = |y|.
It is given that point lies on line 3x + 5y = 15.
It means that point will be the intersecting point of line |x| = |y| and 3x + 5y = 15.
Technique 1
Calculating intersecting point,
|x| = |y| gives us two lines for calculation of point.
These two lines are :-
y = x
y = -x
We will put the value of 'y' as per above data in given equation 3x + 5y = 15 and calculate the points.
Putting y = x in given equation of line,
3x + 5y = 15
3x + 5x = 15
8x = 15
x = 15/8
So, first possible point could be (15/8, 15/8).
Putting y = -x in given equation of line,
3x + 5y = 15
3x + 5(-x) = 15
3x - 5x = 15
-2x = 15
x = -15/2
So, second possible point could be (-15/2, 15/2).
Now,
(15/8, 15/8) lies in 1st quadrant.
(-15/2, 15/2) lies in 2nd quadrant.
Technique 2
Draw the graph for given lines and observe the intersection points.
Graph is attached.
We can observe that there are only two possible points which lie on the line 3x + 5y = 15 and |y|=|x|.
Points are :-
(15/8, 15/8) lying in 1st quadrant and (-15/2, 15/2) lying in 2nd quadrant.
Answer :
So, points which satisfy the given condition lies in 1st and 2nd quadrant only. Hence, option 3 is correct option.
