Q5 of 319 Page 23

Write the distance the lines 4x + 3y – 11 = 0 and 8x + 6y – 15 = 0.

Given:

Lines 4x + 3y – 11 = 0 and 8x + 6y – 15 = 0

To find:

Distance between lines.

Explanation:

The distance between the two parallel lines ax + by + c₁ = 0 and ax + by + c₂ = 0 is
the given lines can be written as

4x + 3y − 11 = 0 … (1)

8x + 6y – 15 = 0

⇒ … (2)

Let d be the distance between the lines (1) and (2).

Hence,

If the centroid of a triangle formed by the points (0, 0), (cos θ, sin θ) and (sinθ, - cosθ) lies on the line y = 2x, then write the value of tanθ.

Write the value of for which area of the triangle formed by points O(0, 0), A(a cos θ, b sin θ) and (a cos θ, - b sin θ) is maximum.

Write the coordinates of the orthocenter of the triangle formed by the lines xy = 0 and x + y = 1

If the lines x + ay + a = 0, bx + y + b = 0 and cx + cy + 1 = 0 are concurrent then write the value of 2abc – ab – bc – ca.