The L1 and L2 denoted by 3 x2+10 x y+8 y2+14 x+22 y+15 =0 intersect at the point P and have gradients m 1 and m 2 respectively. The acute angles between them is θ. Which of the following relations hold good?

Question

The L1 and L2 denoted by 3 x2+10 x y+8 y2+14 x+22 y+15 =0 intersect at the point P and have gradients m 1 and m 2 respectively. The acute angles between them is θ. Which of the following relations hold good? (A) m 1+ m 2=5 / 4 (B) m 1 m 2=3 / 8 (C) acute angle between L1 and L2 is sin -1 (2/5 √5) (D) sum of the abscissa and ordinate of the point P is -1.

Tardigrade Admin · Accepted Answer

f ( x , y )=( x +2 y +3)(3 x +4 y +5) m 1+ m 2=-(2 h / b )=-(10/8)=(-5/4) m 1 m 2=( a / b )=(3/8) Also L 1 and L 2 intersect at (1,-2) ∴ Sum of abscissa and ordinate =-1 tan θ=(2 √ h 2- ab / a + b )=(2 √25-24/11)=(2/11) sin θ=(2/5 √5) ⇒ θ= sin -1((2/5 √5))

Q. The $L_{1}$ and $L_{2}$ denoted by $3 x^{2} + 10 x y + 8 y^{2} + 14 x + 22 y + 15$ $= 0$ intersect at the point $P$ and have gradients $m_{1}$ and $m_{2}$ respectively. The acute angles between them is $θ$ . Which of the following relations hold good?

$m_{1} + m_{2} = 5/4$

$m_{1} m_{2} = 3/8$

acute angle between $L_{1}$ and $L_{2}$ is $sin^{- 1} \frac{2}{5 5}$

sum of the abscissa and ordinate of the point $P$ is $- 1$ .

Q. The L1​ and L2​ denoted by 3x2+10xy+8y2+14x+22y+15 =0 intersect at the point P and have gradients m1​ and m2​ respectively. The acute angles between them is θ. Which of the following relations hold good?

m1​+m2​=5/4

m1​m2​=3/8

acute angle between L1​ and L2​ is sin−155​2​

sum of the abscissa and ordinate of the point P is −1.

f(x,y)=(x+2y+3)(3x+4y+5) m1​+m2​=−b2h​=−810​=4−5​ m1​m2​=ba​=83​ Also L1​ and L2​ intersect at (1,−2) ∴ Sum of abscissa and ordinate =−1 tanθ=a+b2h2−ab​​=11225−24​​=112​ sinθ=55​2​ ⇒θ=sin−1(55​2​)

Q. The $L_{1}$ and $L_{2}$ denoted by $3 x^{2} + 10 x y + 8 y^{2} + 14 x + 22 y + 15$ $= 0$ intersect at the point $P$ and have gradients $m_{1}$ and $m_{2}$ respectively. The acute angles between them is $θ$ . Which of the following relations hold good?

$m_{1} + m_{2} = 5/4$

$m_{1} m_{2} = 3/8$

acute angle between $L_{1}$ and $L_{2}$ is $sin^{- 1} \frac{2}{5 5}$

sum of the abscissa and ordinate of the point $P$ is $- 1$ .