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If the circles x^(2) + y^(2) + 5 Kx + 2y...

If the circles `x^(2) + y^(2) + 5 Kx + 2y + K = 0` and `2x^(2) + y^(2)) + 2Kx + 3y - 1 = 0, (K in R)` intersect at the point P and Q then the line `4x + 5y - K = 0` passes P and Q for :

A

exactly one value of K

B

infinitely many values of K

C

no values of K

D

exactly two values of K

Text Solution

Verified by Experts

The correct Answer is:
C
Equation of common chord is given by `S_(1)-S_(2)=0`
Here equation of common chord is given by
`4kx + 1/2y + k + 1/2 =0`……….(i)
Now this line (i) must be identical to
`4x + 5y -k=0`………(ii)
Dividing (i) by k
`4x + 1/(2k)y + 1+1/(2k)=0`..........(iii)
On comparing (i) and (iii)
`1/(2k)= 5` and `-k = 1+1/(2k), k=1/10` and `-2k^(2) = 2k+1`
`k=1/10` and `2k^(2) + 2k+1=0` has imaginary roots.
No value of k.
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