Let PQ be the common chord of the circles S1:x2+y2+2x+3y+1=0 and S2:x2+y2+4x+3y+2=0 , then the perimeter (in units) of the triangle (. where, .C1=(-1, (-3/2)))

Question

Let PQ be the common chord of the circles S1:x2+y2+2x+3y+1=0 and S2:x2+y2+4x+3y+2=0 , then the perimeter (in units) of the triangle (. where, .C1=(-1, (-3/2))) (A) (9/2) (B) 2√2+3 (C) 3√2+2 (D) (3/2)+2√2

Tardigrade Admin · Accepted Answer

Equation of the common chord is 2x+1=0 <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-qsqusvjqn7jp.png" /> C1M=|(- 2 + 1/2)|=(1/2) PM=√(9/4) - (1/4)=√2 Length of the common chord =2√2 Hence, the perimeter of Δ C1PQ=(3/2)+(3/2)+2√2 =3+2√2 units

Q. Let $PQ$ be the common chord of the circles $S_{1} : x^{2} + y^{2} + 2 x + 3 y + 1 = 0$ and $S_{2} : x^{2} + y^{2} + 4 x + 3 y + 2 = 0$ , then the perimeter (in units) of the triangle $($ where, $C_{1} = (- 1, \frac{- 3}{2}))$

$\frac{9}{2}$

$22 + 3$

$32 + 2$

$\frac{3}{2} + 22$

Equation of the common chord is $2 x + 1 = 0$

$C_{1} M = ∣ ∣ \frac{- 2 + 1}{2} ∣ ∣ = \frac{1}{2}$
$PM = \frac{9}{4} - \frac{1}{4} = 2$
Length of the common chord $= 22$
Hence, the perimeter of $Δ C_{1} PQ = \frac{3}{2} + \frac{3}{2} + 22$
$= 3 + 22$ units

Q. Let PQ be the common chord of the circles S1​:x2+y2+2x+3y+1=0 and S2​:x2+y2+4x+3y+2=0 , then the perimeter (in units) of the triangle ( where, C1​=(−1,2−3​))

29​

22​+3

32​+2

23​+22​