If the sum of the slopes of the pair of lines | vedclass

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

Question

(B) Comparing the given equation $4x^2 + 2hxy - 7y^2 = 0$ with the standard form $ax^2 + 2hxy + by^2 = 0$,we get $a = 4$,$2h = 2h$,and $b = -7$.Let $m

Vedclass · Accepted Answer

$-2$

Vedclass · Answer

(B) Comparing the given equation $4x^2 + 2hxy - 7y^2 = 0$ with the standard form $ax^2 + 2hxy + by^2 = 0$,we get $a = 4$,$2h = 2h$,and $b = -7$.Let $m_1$ and $m_2$ be the slopes of the pair of lines.The sum of the slopes is $m_1 + m_2 = -\frac{2h}{b} = -\frac{2h}{-7} = \frac{2h}{7}$.The product of the slopes is $m_1m_2 = \frac{a}{b} = \frac{4}{-7}$.Given that the sum of the slopes is equal to the product of the slopes,we have $m_1 + m_2 = m_1m_2$.Substituting the values,we get $\frac{2h}{7} = \frac{4}{-7}$.Multiplying both sides by $7$,we get $2h = -4$.Therefore,$h = -2$.

If the sum of the slopes of the pair of lines represented by $4x^2 + 2hxy - 7y^2 = 0$ is equal to the product of the slopes,then the value of $h$ is

Similar Questions

$A$ pair of straight lines drawn through the origin forms an isosceles triangle right-angled at the origin with the line $2x + 3y = 6$. The area (in sq. units) of the triangle so formed is

For $a, b, h > 0$,if the slope of one of the lines represented by $a^2 x^2 + 2hxy + b^2 y^2 = 0$ is twice that of the other,then the value of $\frac{h}{ab}$ is

If $4ab = 3h^2$,then the ratio of the slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ is

The equation of the pair of lines passing through the origin and forming an equilateral triangle with the line $3x + 4y - 5 = 0$ is

For what value of $m$ can the equation $y^2 + 2xy + 2x + my - 3 = 0$ be factored into two linear factors?

Vedclass Test Series

Exam Paper Generator

Online Exam Module