STRAIGHT LINE Q A straight line x/a - y/b = 1 passes through the point (8,6) and cuts off - Maths - Straight Lines

Question

STRAIGHT LINE
Q A straight line x/a - y/b = 1 passes through the point (8,6) and
cuts off a triangle of area 12 units from the axes of co-ordinates
Find the equations of the straight line

Rajat Sethi · Accepted Answer

Equation of line : xa-yb=1 ⇒bx-ay =ab (i)At y=0, x=a,i,e
x-intercept =aAt x=0, y=-b,i,e y-intercept =-bArea of triangle
=12⇒12ab =12⇒ab=24 (ii)From equation (i) we have :
bx-ay=24Since, the line passes from point
(8,6),b(8)-a(6)=24⇒4b-3a=12⇒4(24a)-3a=12
(Using(ii))⇒a2+4a-32=0Solving the Q E in a,we
havea=-4±42+4×322a=4,-8When a=4,b=6Equation of line
:6x-4y=24When a=-8,b=-3Equation of line :-3x+8y=24

STRAIGHT LINEQ. A straight line x/a - y/b = 1 passes through the point (8,6) and cuts off a triangle of area 12 units from the axes of co-ordinates. Find the equations of the straight line.

STRAIGHT LINE
Q. A straight line x/a - y/b = 1 passes through the point (8,6) and cuts off a triangle of area 12 units from the axes of co-ordinates. Find the equations of the straight line.