Home
Class 12
MATHS
If the point 3x+4y-24=0 intersects the X...

If the point `3x+4y-24=0` intersects the `X`-axis at the point `A` and the `Y`-axis at the point `B`, then the incentre of the triangle `OAB`, where `O` is the origin, is

A

`(4,3)`

B

`(3,4)`

C

`(4,4)`

D

`(2,2)`

Text Solution

Verified by Experts

Given equation of line is
`3x+4y-24=0`
For intersection with `X`-axis put `y=0`
`implies3x-24=0`
`impliesx=8`
For intersection with `Y`-axis , put `x=0`
`implies4y-24=0impliesy=6`
`:. A(8,0)` and `B(0,6)`

Let `AB=c=sqrt(8^(2)+6^(2))=10`
`OB=a=6`
and `OA=b=8`
Also, let incentre i `(h,k)`, then
`h=(ax_(1)+bx_(2)+cx_(3))/(a+b+c)`(here , `x_(1)=8`, `x_(2)=0`, `x_(3)=0`)
`=(6xx8+8xx0+10xx0)/(6+8+10)=(48)/(24)=2`
and `k=(ay_(1)+by_(2)+cy_(3))/(a+b+c)` (here, `y_(1)=0`, `y_(2)=6`, `y_(3)=0`)
`=(6xx0+8xx6+10xx0)/(6+8+10)=(48)/(24)=2`
`:.` Incentre is `(2,2)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

The line 4x+3y-12=0 meets the x-axis at the point……….

A line 4x+3y=24 cut the x-axis at point A and cut the y-axis at point B then incentre of triangle OAB is (a) (4,4) (b) (4,3) (c) (3,4) (d) (2,2)

The line 6x+8y=48 intersects the coordinates axes at A and B, respecively. A line L bisects the area and the perimeter of triangle OAB, where O is the origin. The slope of line L can be

The line 6x+8y=48 intersects the coordinates axes at A and B, respecively. A line L bisects the area and the perimeter of triangle OAB, where O is the origin. Slope of Line L is

A straight line through the point (2, 2) intersects the lines sqrt3 x + y = 0 and sqrt3 x - y = 0 at the points A and B. The equation of AB so that the triangle OAB is equilateral, where O is the origin.

The circle x^2 + y^2 - 3x - 4y + 2 = 0 cuts the x axis at the points

Statement 1 :If the lines 2x+3y+19=0 and 9x+6y-17=0 cut the x-axis at A ,B and the y-axis at C ,D , then the points, A , B , C , D are concyclic. Statement 2 : Since O A x O B=O C x O D , where O is the origin, A , B , C , D are concyclic.

Through the point P(3,4) a pair of perpendicular lines are dranw which meet x-axis at the point A and B. The locus of incentre of triangle PAB is

Take a point A on X-axis and B on Y-axis and find area of the triangle AOB. Discuss with your friends how they do it?

A circle is drawn through the point of intersection of the parabola y=x^(2)-5x+4 and the x-axis such that origin lies outside it. The length of a tangent to the circle from the origin is ________ .