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