Question

Find the equation of the circle whose centre is (3, -2) and which cuts off an intercept of length 6 on the line 4x - 3y + 2 =0

Answer 1

Answer:

rrect option is

C

x

2

+y

2

−6x+4y−21=0

Given,

4x−3y+2=0

(3,−2)

Length of perpendicular,

=

4

2

+(−3)

2

4×3−3×(−2)+2

=

5

20

=4

Now, the circle cuts the intercept of length 6 at a distance of 3 on each side

Hence radius of circle is,

5

2

+3

2

=

34

Hence the equation of circle is,

(x−3)

2

+(y+2)

2

=34

x

2

−6x+y

2

+4y−21=0