QJEEM19Maedaf: JEE Main 2019 Mathematics - Class 11 JEEM19Maedaf Solution: Suppose that the points (h,k), (1,2) and (–3,4) lie on the line …

Equation of line L₁ passing through points (1, 2) and (–3, 4) is :

y - 2 = $\left( {{{4 - 2} \over { - 3 - 1}}} \right)$ (x - 1)

$\Rightarrow$ y - 2 = $- {1 \over 2}$ (x - 1)

$\Rightarrow$ 2y – 4 = –x + 1

$\Rightarrow$ x + 2y = 5 .......(L₁)

Line L₁ passes through point (h, k).

$\therefore$ h + 2k = 5 .......(1)

Line L₂ is perpendicular to line L₁.

$\therefore$ Equation of line L₂ :

2x - y = $\lambda$

This line L₂ passes through point (4, 3).

$\therefore$ 2(4) - 3 = $\lambda$

$\Rightarrow$ $\lambda$ = 5

$\therefore$ Line L₂ :

2x - y = 5

L₂ also passes through (h, k)

$\therefore$ 2h - k = 5 ............(2)

Solving (1) and (2) we get,

h = 3 and k = 1

$\therefore$ ${k \over h} = {1 \over 3}$