First slide

Definition of a circle

Question

The radius of the largest circle lying in the first quadrant and touching $4 x + 3 y = 12$ and co-ordinate axes is

Moderate

A

5
B

6
C

7
D

8

Solution

Given line is $4 x + 3 y = 12$ ….(1)
Since the radius of the largest circle lying in the first quadrant then centre is $C (r, r)$ .

Since the circle touches the line then

$r = d$ =The perpendicular distance from centre to the line.

$\Rightarrow r = \frac{| 4 r + 3 r - 12 |}{\sqrt{16 + 9}}$

$\Rightarrow 5 r = | 7 r - 12 |$

$\Rightarrow 7 r - 12 = \pm 5 r$

$\Rightarrow r = 1, 6$ .

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