...it be required to determine its equation. A straight line is determined geometrically ; first, if it pass through a given point and make a given angle with a given straight line or axis : secondly, if it pass through two given points. 19. For the first case. Let a and 3 be the...

...order that they may be at right angles to one another, we must have tan <p = co , or 1 + mm' = 0. 26. To find the equations to the straight lines which...and make a given angle with a given straight line. Let BT (fig. 8) be the given line, and y = mx + c its equation, therefore tan PTA =m; B"!* one of the...

...axes and explain the meaning of the constants. 2. Find the equation to a straight line which shall pass through a given point and make a given angle with a given line. Ex. Through the point (0, 0) making an angle of 90° with the line x + y = a. 4. Find the equation...

...(xl, yj, is (2). If (2) is perpendicular to (1), we have m'm +1=0. Hence the required equation is 1 , 45. To find the equations to the straight lines which...+ c. Suppose CD and CE the two lines which can be diawn through C, each making an angle /3 with AB. Then tan CDX = tan (BAX + /3) _ m + tan/3 1 — m...

...t•• \ /• If (2) is perpendicular to (1), we have mm +1=0. Hence the required equation is 1 ' ' m ' 45. To find the equations to the straight lines which...and make a given angle with a given straight line. Let AB be the given straight line ; C the given point ; h, k, its co-ordinates ; /3 the given angle....

...angles. Hence, deduce the expression for the cosine of an angle of a triangle in terms of the sides. 13. Find the equations to the straight lines which pass...and make a given angle with a given straight line. Example. Find the equations to the lines which pass through the origin, and are inclined at an angle...

...16. в = а. 17. rcos(0-a)=^). 18. rcos0 + 5rsin0 = 6ti. 19. If the axes be inclined at an angle <a, find the equations to the straight lines which pass through a given point on the axis of x, and are perpendicular to the axes. 20. Find the equation to the straight line which...

...the several cases in which 62 is greater than, equal to, or less than ac ? 12. Find the equations of the straight lines which pass through a given point...and make a given angle with a given straight line. What are the equations of the straight lines which pass through the centre of the circle — and are...

...the condition of the next article, only one line is possible. 26. To find the equations to the two straight lines which pass through a given point and make a given angle (/3} with a given straight line (y=mx + b), the axes being rectangular. m± tan/3 . The equations are...

...angles. Hence, deduce the expression for the cosine of an angle of a triangle in terms of the. sides. 13. Find the equations to the straight lines which pass...and make a given angle with a given straight line. Example. Find the equations to the lines which pass through the origin, and are inclined at an angle...