Question

If the line 4x+3y+1=0 cuts the axes at a and b, then the equation of perpendicular bisector of ab is

Answer 1

line 4x + 3y + 1 = 0 cuts the axes at a and b.

if it cuts x-axis, y = 0

then, 4a + 0 + 1 = 0 ⇒x = -1/4

so, point a (-1/4, 0)

and if cuts y-axis , x = 0

then, 0 + 3b + 1 = 0 ⇒b = -1/3

so, point b(0, -1/3)

now slope of line ab = (-1/3 - 0)/{0 - (-1/4)} = (-1/3)/(1/4) = 4/-3

so, slope of perpendicular on line ab, m = -1/slope of line ab

= -1/(-4/3) = 3/4

let c is bisecting line ab. so, c = [(-1/4 + 0)/2, {0 + (-1/3)}/2 ]

= (-1/8, -1/6)

so, equation of required line,

(y + 1/6) = (3/4)(x + 1/8)

⇒4(y + 1/6) = 3(x + 1/8)

⇒4y + 4/6 = 3x + 3/8

⇒3x - 4y + (3/8 - 4/6) = 0

⇒3x - 4y - 14/48 = 0

⇒72x - 96y - 7 = 0 [Ans]

Answer 2

using point and slope we can find equation by the following way take any point and assume it as x, y now our actual point will be the given pointSona the given point y-coordinate minus y and the given point x co-ordinate - xwill be divided and that will be equal to the slope