Question

The equation of the line passing through $(2,\frac{\pi }{4})$ and parallel to $3\cos \theta +4\sin \theta =\frac{5}{r}$ is

• A. $3\cos \theta +4\sin \theta =\frac{7}{r}$
• B. $3\cos \theta +4\sin \theta =\frac{3\sqrt{2}}{r}$
• C. $3\cos \theta +4\sin \theta =\frac{4\sqrt{2}}{r}$
• D. $3\cos \theta +4\sin \theta =\frac{7\sqrt{2}}{r}$

Answer 1

The correct option is D $3\cos \theta +4\sin \theta =\frac{7\sqrt{2}}{r}$

Given equation of line
$3\cos \theta +4\sin \theta =\frac{5}{r}$
Equation of line parallel to given line is
$3\cos \theta +4\sin \theta =\frac{k}{r}$
Since, it passes through $(2,\frac{\pi }{4})$
$\Rightarrow k=7\sqrt{2}$
So, the required equation of line is
$3\cos \theta +4\sin \theta =\frac{7\sqrt{2}}{r}$