If the sum of slopes of lines represented by | vedclass

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

Question

(A) The given equation is $ax^2+8xy+5y^2=0$. Comparing this with the general equation $Ax^2+2Hxy+By^2=0$,we have $A=a$,$2H=8$ (so $H=4$),and $B=5$. Le

Vedclass · Accepted Answer

-$4$

Vedclass · Answer

(A) The given equation is $ax^2+8xy+5y^2=0$. Comparing this with the general equation $Ax^2+2Hxy+By^2=0$,we have $A=a$,$2H=8$ (so $H=4$),and $B=5$. Let the slopes of the lines be $m_1$ and $m_2$. The sum of slopes is $m_1+m_2 = -\frac{2H}{B} = -\frac{8}{5}$. The product of slopes is $m_1m_2 = \frac{A}{B} = \frac{a}{5}$. According to the given condition,the sum of slopes is twice their product: $m_1+m_2 = 2(m_1m_2)$ $-\frac{8}{5} = 2\left(\frac{a}{5}\right)$ $-\frac{8}{5} = \frac{2a}{5}$ $2a = -8$ $a = -4$.

If the sum of slopes of lines represented by $ax^2+8xy+5y^2=0$ is twice their product,then $a=$

Similar Questions

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 one of the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ bisects the angle between the coordinate axes in the first quadrant,then which of the following is true?

The combined equation of the pair of lines passing through the origin and perpendicular to the pair of lines $2x^2 - xy - y^2 = 0$ is:

The equation to the pair of straight lines through the origin which are perpendicular to the lines $2x^2 - 5xy + y^2 = 0$ is:

The auxiliary equation of the lines passing through the origin and having slopes $\sqrt{3}+1$ and $\sqrt{3}-1$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module