(5, 3) and (cosq, sin q) lie on the same side of the line 2... | MATH - QUESTIONS RELATED TO GEOMETRICAL CONDITIONS | SolveeIt | Solveeit

Today, August 23

Question

(5, 3) and (cosq, sin q) lie on the same side of the line

2x + y = 8 then q lies between-

A

(0, 2p)

B

(–p, p)

C

$\left( 0,\frac{\pi}{2} \right)$

D

None of these

Answer

None of these

Explanation

Solution

If (5, 3) & (cos q, sin q) lie on the same side of

the line 2x + y – 8 = 0 then {2(5) + 3 – 8}

{2 cos q + sin q – 8} > 0 Ž (2cosq + sin q – 8) > 0

Q if f(q) = 2 cos q + sin q

\ f(q)_max = $\sqrt{2^{2} + 1}$ = $\sqrt{5}$

Ž This relation can never be positive.