The polar equation $\cos \theta + 7 \sin \theta = \frac{1}{r}$ represents a

The equation of a straight line passing through $(-3, 2)$ and cutting an intercept equal in magnitude but opposite in sign from the axes is given by:

Find the equation of the line passing through the point $(4, 3)$ such that the sum of its intercepts on the axes is $-1$.

If the line $y = mx + c$ passes through the points $(2, 4)$ and $(3, -5)$,then:

The equation of the line which makes a right-angled triangle with the axes whose area is $6$ sq. units and whose hypotenuse is $5$ units,is

In what direction should a line be drawn through the point $(1, 2)$ so that its point of intersection with the line $x + y = 4$ is at a distance of $\frac{\sqrt{6}}{3}$ from the given point (in $^\circ$)?