Question

The line 4y - 3x + i=0 touches the
circle x' + y - 4x - 8y- 5=0 then i =?​

Answer 1

Step-by-step explanation:

If line 4y−3x+λ=0 touches the circle x

2

+y

2

−4x−8y−5=0 then distance of its centre from the line is equal to its radius.

Centre is (−2,−4)

radius =

4+16+5

=

25

=5 units

∴ 5=

a

2

+b

2

ax

1

+by

1

+c

5=

16+9

∣6−16+λ∣

⇒5=

5

∣−10+λ∣

⇒

5

λ−10

=±5⇒λ−10=25

⇒λ=10+10=35

5

λ−10

=−5⇒λ−10=−25⇒λ=−15

∴ λ=−15,25

HOPE IT HELPS YOU

Answer 2

Answer:

ANSWER

If line 4y−3x+λ=0 touches the circle x

2

+y

2

−4x−8y−5=0 then distance of its centre from the line is equal to its radius.

Centre is (−2,−4)

radius =

4+16+5

=

25

=5 units

∴ 5=

a

2

+b

2

ax

1

+by

1

+c

5=

16+9

∣6−16+λ∣

⇒5=

5

∣−10+λ∣

⇒

5

λ−10

=±5⇒λ−10=25

⇒λ=10+10=35

5

λ−10

=−5⇒λ−10=−25⇒λ=−15

∴ λ=−15,25