Question

Equation of a circle whose centre is (3,-1) which cut off an intercept of length 6 unit from the line 2x-5y+18=0 is

Answer 1

The length of perpendicular from

(

3

,

−

1

)

to

2

x

−

5

y

+

18

=

0

is

∣

∣

∣

∣

2

×

3

−

5

×

(

−

1

)

+

18

√

2

2

+

5

2

∣

∣

∣

∣

=

29

√

29

=

√

29

Now as circle cuts off an intercept of length

6

, it intercepts at a distance of

3

on each side from the foot of the perpendicular.

Hence radius of circle is

√

(

√

29

)

2

+

3

2

=

√

38

and equation of circle is

(

x

−

3

)

2

+

(

y

+

1

)

2

=

38

or

x

2

+

y

2

−

6

x

+

2

y

−

28

=

0

graph{(x^2+y^2-6x+2y-28)(2x-5y+18)((x-3)^2+(y+1)^2-0.03)=0 [-9.75, 10.25, -4.04, 6.38]}