Question

if the line 2x-y+k=0 is a diameter of the circle x^2+y^2+6x-6y+5=0, the k is equal to ??
a) 5
b) -4
c) 7/2
d) 9

Answer 1

GIVEN :

The equation of the line 2x-y+k=0 is a diameter of the circle $x^2+y^2+6x-6y+5=0$

TO FIND :

The value of k

SOLUTION :

Given equation of the circle is $x^2+y^2+6x-6y+5=0\hfill (1)$

The general form of the circle is $x^2+y^2+2gx+2fy+c=0\hfill (2)$

Comparing the equation (1) and (2)

2g=6             2f=-6

⇒ g=3        ⇒  f=-3

The formula for the centre of the circle is (-g,-f)

(-3,-(-3)

⇒ the centre is (-3,3)

The centre (-3,3) of the circle lies on the given line (diameter ) 2x-y+k=0

Put x=-3 and y=3 in 2x-y+k=0

2(-3)-(3)+k=0

-6-3+k=0

-9+k=0

k=9

∴ The value of k in the given equation 2x-y+k=0 is 9

∴  the value of k is 9

Option d) 9 is correct.