Question

If a b c are in gp then the area of the triangle formed by the line ax+by+c=0 with the coordinate axes is equal to

Answer 1

Answer:

1/2

Step-by-step explanation:

Hi,

Given that a, c and b are in G.P

⇒ c² = ab

Given equation of the line is ax + by + c = 0

Let the points of intersection of the line with the coordinate axes

be A and B

Coordinates of point of intersection of line with x-axis A are

( -c/a, 0)

Coordinates of point of intersection of line with y-axis B are

(0, -c/b)

Area of the triangle formed by the line with the coordinate axes

= 1/2*base * height of triangle

= 1/2*|-c/a|*|-c/b|

= 1/2*|c²/ab|

But since a ,c and b are in G.P, we have c² = ab

So, area of the triangle = 1/2 sq.units

Hope, it helps !