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Need clarity, kindly explain! - If the line intersects the x-axis at the point A and the y-axis at the point B,then the incentre of - Co-ordinate geometry - JEE Main

If the line 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:

  • Option 1)

    (3,4)

  • Option 2)

    (2,2)

  • Option 3)

    (4,3)

  • Option 4)

    (4,4)

Answers (1)
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A admin

 

y-intercept -

The distance on the y-axis from the origin where the straight line cuts it.

- wherein

 

From the fig (r,r) is the center of circle.

Distance from point (r,r) to the line 3x+4y-24=0

\left | \frac{3r+4r-24}{\sqrt{9+16}} \right |=r

7r-24=\pm 5r

r=14\: \: or \: \: r=2

centre is (2,2)


Option 1)

(3,4)

Option 2)

(2,2)

Option 3)

(4,3)

Option 4)

(4,4)

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