- Different forms of Ax + By + C = 0 - Slope-intercept form, Intercept form, Normal form
Prove that the product of the lengths of the perpendiculars drawn from the points
`(sqrt(a^2 - b^2),0)` and `(-sqrta^2-b^2,0)` to the line `x/a cos theta + y/b sin theta = 1` is `b^2`
Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.
i) `x – sqrt3y + 8 = 0`
(ii) y – 2 = 0
(iii) x – y = 4
Find the equation of the line passing through the point of intersection of the lines 4x + 7y – 3 = 0 and 2x– 3y + 1 = 0 that has equal intercepts on the axes.
In the triangle ABC with vertices A (2, 3), B (4, –1) and C (1, 2), find the equation and length of altitude from the vertex A.
Reduce the following equations into intercept form and find their intercepts on the axes.
(i) 3x + 2y – 12 = 0
(ii) 4x – 3y = 6
(iii) 3y + 2 = 0