Question

The distance of the tangent to the circle x² + y2 - 6x + y - 1 = 0 at the point (1,2)
from origin is​

Answer 1

Answer:

Given equation of circle is

x

2

+y

2

−6x−8y+21=0,

whose centre =(3,4)

and radius =

9+16−21

=2

Clearly, the line AB is chord of contact and its equation is

xx

1

+yy

1

+g(x+x

1

)+f(y+y

1

)+c=0

Here, (x

1

,y

1

)=(0,0)

∴0+0−3(x+0)−4(y+0)+21=0

⇒3x+4y−21=0 ....(i)

Now, perpendicular distance from (3,4) to the line (i) is

CM=

9+16

3(3)+4(4)−21

=

5

4

AM=

AC

2

−CM

2

=

4−

25

16

=

5

2

21

∴AB=2AM=

5

4

21