If the slope of one of the lines in the pair | vedclass

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

Question

(A) The given equation is $8x^2 + axy + y^2 = 0$. Let the slopes of the two lines be $m_1$ and $m_2$. For a homogeneous equation $Ax^2 + Bxy + Cy^2 =

Vedclass · Accepted Answer

$8 \sqrt{\frac{2}{3}}$

Vedclass · Answer

(A) The given equation is $8x^2 + axy + y^2 = 0$. Let the slopes of the two lines be $m_1$ and $m_2$. For a homogeneous equation $Ax^2 + Bxy + Cy^2 = 0$,the sum of slopes is $m_1 + m_2 = -B/C$ and the product of slopes is $m_1 m_2 = A/C$. Here,$A = 8$,$B = a$,and $C = 1$. So,$m_1 + m_2 = -a$ and $m_1 m_2 = 8$. Given that one slope is thrice the other,let $m_1 = 3m_2$. Substituting this into the product equation: $(3m_2) 	imes m_2 = 8$ $\Rightarrow 3m_2^2 = 8$ $\Rightarrow m_2^2 = 8/3$. Substituting into the sum equation: $3m_2 + m_2 = -a$ $\Rightarrow 4m_2 = -a$ $\Rightarrow m_2 = -a/4$. Squaring both sides: $m_2^2 = a^2/16$. Equating the two values of $m_2^2$: $a^2/16 = 8/3$ $\Rightarrow a^2 = 128/3$ $\Rightarrow a = \pm \sqrt{128/3} = \pm 8 \sqrt{2/3}$. Since the options provide the positive value,$a = 8 \sqrt{\frac{2}{3}}$.

If the slope of one of the lines in the pair of lines $8x^2 + axy + y^2 = 0$ is thrice the slope of the other line,then $a =$

Similar Questions

If the slopes of the lines represented by $K x^2 + 5 x y + y^2 = 0$ differ by $1$,then $K =$

If one of the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ is coincident with one of the lines represented by $a'x^2 + 2h'xy + b'y^2 = 0$,then:

If the slope of one of the lines given by $ax^2+2hxy+by^2=0$ is two times the other,then

If the slope of one of the lines represented by $ax^2+2hxy+by^2=0$ is twice that of the other,then $h^2:ab$ is

If $m_1$ and $m_2$ are the slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ satisfying the condition $16h^2 = 25ab$,then $\ldots$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module