Question

if the line's 3x-4y+4= and 6x-8y+7= are tangents to a circle then find the radius of the circle​

Answer 1

Answer:

Equation of the given tangents are-

t

1

:3x−4y+4=0

t

2

:6x−8y−7=0⇒3x−4y−

2

7

=0

Here,

a=3,b=−4,c

1

=4,c

2

=−

2

7

Since slopes of the given tangents are equal, i.e.,

4

3

∴ the given tangents are parallel.

As we know that, the distance between two parallel lines given by,

d=

a

2

+b

2

∣c

2

−c

1

∣

∴ distance between t

1

&t

2

=

3

2

+(−4)

2

∣

∣

∣

∣

∣

∣

4−(−

2

7

)

∣

∣

∣

∣

∣

∣

=

9+16

(

2

15

)

=

2×5

15

=

2

3

As we know that distance between two parallel tangents of a circle is equal to the diameter of that circle.

∴ diameter of given circle =

2

3

∴ Radius of the given circle =

2

diameter

=

2

(

2

3

)

=

4

3

Hence, the radius of the given circle is

4

3

.