The system of equations $4 x+6 y=5$ and $8 x+12 y=10$ has

A line passes through $(-1,-3)$ and perpendicular to $x+6 y=5$. Its $x$ intercept is

The angle between the line $x+y=3$ and the line joining the points $(1,1)$ and $(-3,4)$ is

A line passes through $$(2,2)$$ and is perpendicular to the line $$3 x+y=3$$. Its $$y$$-intercept is

If the straight line $$2 x-3 y+17=0$$ is perpendicular to the line passing through the points $$(7,17)$$ and $$(15, \beta)$$, then $$\beta$$ equals

If the vertices of a triangle are $$(-2,6),(3,-6)$$ and $$(1,5)$$, then the area of the triangle is

The equation of straight line which passes through the point $$\left(a \cos ^3 \theta, a \sin ^3 \theta\right)$$ and perpendicular to $$x \sec \theta+y \operatorname{cosec} \theta=a$$ is

The two lines $$l x+m y=n$$ and $$l^{\prime} x+m^{\prime} y=n^{\prime}$$ are perpendicular if

A line cuts off equal intercepts on the co-ordinate axes. The angle made by this line with the positive direction of $$X$$-axis is