+91-87964 74404
FlagBACK
Question icon
Grade 12th passAnalytical Geometry

A line passing through (3,4) meets the coordinate axes at A and B.then the maximum area of the triangle OAB is......

Profile image of Pabba Somanna
10 Years agoGrade 12th pass
Answers icon

1 Answer

Profile image of Vikas TU
10 Years ago
Let the line be y = mx + c
passing through 3,4 
the eqn. becomes ------>
4 = 3m +c-----------------------(A)
Area of triangle = -0.5 x c/m x c
                       = -0.5 x c^2/m
 
From eq. (A) substitute here,
f(c) let = 1.5c^2/(c-4)
          form maximum f'(c) = 0
(2c(c-4) – c^2))/(c-4)^2 = 0
c^2 – 8c =0
c(c-8) =0
c = 0  or c =8
at c=8
Area of triangle = 24.sq. units.         

Other Related Questions on analytical geometry

question mark
  • The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is 
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius. 
 
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
analytical geometry
1 Answer Available

Last Activity: 4 Years ago