A pair of lines S=0 together with the lines g | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The given pair of lines is $8 x^2-14 x y+3 y^2+10 x+10 y-25=0$.Factoring the expression,we get $(4 x-y-5)(2 x-3 y+5)=0$.The lines are $L_1: 4 x-y-

Vedclass · Accepted Answer

$8 x^2-14 x y+3 y^2-50 x+50 y+75=0$

Vedclass · Answer

(C) The given pair of lines is $8 x^2-14 x y+3 y^2+10 x+10 y-25=0$.Factoring the expression,we get $(4 x-y-5)(2 x-3 y+5)=0$.The lines are $L_1: 4 x-y-5=0$ and $L_2: 2 x-3 y+5=0$.The intersection point of $L_1$ and $L_2$ is $(2,3)$.Let the pair of lines $S=0$ be $(4 x-y+c_1)(2 x-3 y+c_2)=0$.Since these lines form a parallelogram with $L_1$ and $L_2$,the diagonals intersect at $(3,2)$.The intersection of the new pair of lines is $(x_1, y_1)$. The midpoint of $(2,3)$ and $(x_1, y_1)$ is $(3,2)$.Thus,$\frac{x_1+2}{2}=3 \Rightarrow x_1=4$ and $\frac{y_1+3}{2}=2 \Rightarrow y_1=1$.Substituting $(4,1)$ into the lines $4 x-y+c_1=0$ and $2 x-3 y+c_2=0$,we get $c_1=-15$ and $c_2=-5$.The equation $S=0$ is $(4 x-y-15)(2 x-3 y-5)=0$.Expanding this,we get $8 x^2-14 x y+3 y^2-50 x+50 y+75=0$.

$A$ pair of lines $S=0$ together with the lines given by the equation $8 x^2-14 x y+3 y^2+10 x+10 y-25=0$ form a parallelogram. If its diagonals intersect at the point $(3,2)$,then the equation $S=0$ is

Similar Questions

The electronic configurations of $Cr^{2+}, Mn^{2+}, Fe^{2+},$ and $Ni^{2+}$ are $3d^4, 3d^5, 3d^6,$ and $3d^8$ respectively. Which one of the following aqua complexes will exhibit the minimum paramagnetic behavior?

Work done to increase the temperature of one mole of an ideal gas by $30^{\circ} C$,if it is expanding under the condition $V \propto T^{2/3}$ is,$(R = 8.314 \ J/mol \cdot K)$ (in $J$)

In the given circuit,the current flowing through the circuit is: (in $A$)

Which of the following factors exclusively affects reproduction in seasonal breeders,both plants and animals?

Which of the following theories provides the latest explanation for the closure of stomata?

Vedclass Test Series

Exam Paper Generator

Online Exam Module