S L Loney Solutions for Chapter: The Straight Line, Rectangular Coordinates, Exercise 1: EXAMPLES V

Find the equation of the straight line passing through the pair of points $(a\cos {\varphi }_1, a\sin {\varphi }_1)$ and $\left(a\cos {\varphi }_2, a\sin {\varphi }_2\right).$

Find the equation to the straight line passing through the pair of points $(a\cos {\varphi }_1, b\sin {\varphi }_1)$ and $\left(a\cos {\varphi }_2, b\sin {\varphi }_2\right).$

Find the equation to the straight line passing through the pair of points $\left(a\sec {\varphi }_1,b\tan {\varphi }_1\right)$ and $(a\sec {\varphi }_2,b\tan {\varphi }_2)$.

Find the equations of the sides of the triangle, the coordinates of whose angular points are respectively $\left(1, 4\right)$, $\left(2, -3\right)$ and $(-1, -2).$

Find the equations to the sides of the triangle the coordinates of whose angular points are, respectively $(\mathrm{0,} 1),$ $(2, 0)$ and $(-1, -2).$

Find the equation to the diagonals of the rectangle the equation of whose sides are $x=a, x=a^{\text{'}}, y=b$ and $y=b^{\text{'}}.$

Find the equation of the straight line which bisects the line joining the points $(a,b)$ and $(a^{\text{'}},b^{\text{'}})$, and also bisects the line joining the points $(-a,b)$ and $\left(a^{\text{'}},-b^{\text{'}}\right).$

Find the equations of the straight lines which passes through the origin and trisect the portion of the straight line $3x+y=12$ which is intercepted between the axes of coordinates.