IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

rohitkuruvila

P(a,b) is the midpoint of a line segment between the axes.show that the equation of the line is x/a +y/b=2

nishantsingh89

(a,b) midpoint of the line segment b/w axes

now let the line intersects y axis at(0,p) and x axis at (q,0)

the eqn of line is

x/q + y/p =1

also by mid poin formula

a = q/2 q=2a

similarly p = 2b

put these values in eqn of line
x/2a + y/2b =1
x/a + y/b =2 answer

karthik2007

The co ordinate of the point where the line meets the x axis is (2a, 0)

Similarly, for the y axis, co ordinate is (0.2b)

(as a,b is the midpoint)

So equation is x/2a + y/2b = 1

or x/a + y/b = 2 (Multiplying by 2)

venkat_tatolu

A line cuts the x axis and y - axis at the

points A and B respectively.If P(h,k) is the

point on the segment AB such that

AP:PB=l:m then the equation of the line is

mx/h+ly/k = l+m.

Now put l=m=1.(Since midpoint) and h=a,

k=b.U get the equation x/a+y/b=2.

payal_bon

Since the line is between the axes so

Let its point at x axis is (p,0)

point at y axis is (0,q)

So the x and y intercepts are p and q respectively.

So by the intercept form the equation is x/p+y/q=1.......(i)

Now the midpoint of the given line is (a,b)

Thereforecoordinates of the midpoint(a,b)are:

a=(p+0)/2 b=(q+0)/2

or, p=2a or, q=2b

Putting theses values in eq(i)

x/p+y/q=1

or, x/2a+y/2b=1

or, 1/2[x/a+y/b]=1

or, x/a+y/b=2 [proved]

Plz do rate me.

euracle

Hey, u see the eqn of line is

x/q + y/p =1

also by mid poin formula

a = q/2 q=2a

similarly p = 2b

put these values in eqn of line
x/2a + y/2b =1
x/a + y/b =2 answer

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