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

Question

Accepted Answer

Correct answer: B. (b) JEE Main 2019 S_1 ≡x^2+y^2+5 Kx+2y+K=0 S_2 ≡x^2+y^2+ Kx+ 32y- 12=0 Equation of common chord is S_1-S_2=0 ⇒4 Kx+ y2+K+ 12=0 … (i) Equation of the line passing through the intersection points P and Q is, 4x+5y-K=0 … (ii) Comparing (i) and (ii), 4K4= 110= 2K+1-2K … (iii) ⇒K= 110and -2K=20K+10 ⇒22K=-10 ⇒K=- 511 ∵K= 110or - 511 is not satisfying equation (iii) ∴ No value of K exists.

$If the circles x^{2} + y^{2} + 5 Kx + 2 y + K = 0 and 2 (x^{2} + y^{2}) + 2 Kx + 3 y - 1 = 0, (K ϵ R), intersect at the points P and Q, then the line 4 x + 5 y - K = 0 passes through P and Q, for :$

Solution

More Circle PYQs