Let y=x+2,4 y=3 x+6 and 3 y=4 x+1 be three tangent lines to the circle (x-h)2+(y- k )2= r 2. Then h + k is equal to :

Question

Let y=x+2,4 y=3 x+6 and 3 y=4 x+1 be three tangent lines to the circle (x-h)2+(y- k )2= r 2. Then h + k is equal to : (A) 5 (B) 5(1+√2) (C) 6 (D) 5 √2

Tardigrade Admin · Accepted Answer

L 1: y = x +2, L 2: 4 y =3 x +6, L 3: 3 y =4 x +1 Bisector of lines L 2 L 3 (4 x-3 y+1/5)=±((3 x-4 y+6/5)) (+) 4 x-3 y+1=3 x-4 y+6 x+y=5 Centre lies on Bisector of 4 x-3 y+1=0 (0) 3 x-4 y+6=0 ⇒ h + k =5

Q. Let $y = x + 2, 4 y = 3 x + 6$ and $3 y = 4 x + 1$ be three tangent lines to the circle $(x - h)^{2} + (y - k)^{2} = r^{2}$ . Then $h + k$ is equal to :

5

$5 (1 + 2)$

6

$52$

Q. Let y=x+2,4y=3x+6 and 3y=4x+1 be three tangent lines to the circle (x−h)2+(y−k)2=r2. Then h+k is equal to :

5

5(1+2​)

6

52​

L1​:y=x+2,L2​:4y=3x+6,L3​:3y=4x+1 Bisector of lines L2​&L3​ 54x−3y+1​=±(53x−4y+6​) (+)4x−3y+1=3x−4y+6 x+y=5 Centre lies on Bisector of 4x−3y+1=0& (0) 3x−4y+6=0 ⇒h+k=5

Q. Let $y = x + 2, 4 y = 3 x + 6$ and $3 y = 4 x + 1$ be three tangent lines to the circle $(x - h)^{2} + (y - k)^{2} = r^{2}$ . Then $h + k$ is equal to :

$5 (1 + 2)$

$52$