Question

the points (4,-2), (3,-b)are conjugate with respect to x^2+y^2=24 then b=​

Answer 1

Answer:

Equation of circle-

x

2

+y

2

−5x+8y+6=0

Polar of point (4,2) is-

S

1

=0

4x+2y−5(

2

x+4

)+8(

2

y+2

)+6=0

4x+2y−

2

5

x−10+4y+8+6=0

3x+12y+8=0.....(1)

Given that the points (4,2) and (k,−3) are conjugaet.

Therefore, Polar of point (4,2) passes through the point (k,−3).

∴3k+12(−3)+8=0

⇒3k=36−8

⇒k=

3

28

Hence the value of k is

3

28

.