Numerical : Find the equation of the line whose perpendicular distance from the origin is 4 units and the angle which the normal makes with positive direction of x-axis is 30 °.
Solution : Here , we are given p = 4 and ω = 30 0 . Using the formula x cos ω + y sin ω = p , we get
x cos 30 o + y sin 30 o = 4 or x * ½ + y * √3 / 2 = 4 or x + √3y -8 = 0
General Equation of Straight line
We know that graph of general equation of first degree in two variables , Ax + By + C = 0 , where A , B and C are real constants such that A and B are not zero simultaneously is a straight line .
Thus General Equation of Straight line is Ax + By + C = 0 , where A , B and C are real constants such that A and B are not zero simultaneously .
Numerical : Equation of a line is 3x – 4y + 10 = 0 . Find its ( i ) slope , ( ii ) x – and y-intercepts .
Solution : To find the slope of the line , we need to rewrite the equation in y = mx + c form .
4y = 3x + 10