JEE Main · 2019 · 08 Apr 2019 · Shift 1 · Straight Lines

A point on the straight line,

3 x + 5 y = 15

which is equidistant from the coordinate axes will lie only in:

(A) $4^{th}$ quadrant
(B) $1^{st}, 2^{nd}$ and $4^{th}$ quadrants
(C) $1^{st}$ quadrant
(D) $1^{st}$ and $2^{nd}$ quadrants✓ Correct

Answer: (D)

Solution

A point equidistant from the two axes lies on

y = x

y = - x

. Intersecting

y = x

with

3 x + 5 y = 15

gives

8 x = 15

, a point

(\frac{15}{8}, \frac{15}{8})

in the first quadrant; intersecting

y = - x

gives

- 2 x = 15

, a point

(- \frac{15}{2}, \frac{15}{2})

in the second quadrant. Both sit above the x-axis, so such points occur only in the first and second quadrants.

JEE Main · 2019 · 08 Apr 2019 · Shift 1 · Single correct option

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