The lines p(p^2 + 1)x - y + q = 0 and (p^2 + | vedclass

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

Question

(A) If two lines are perpendicular to a common line,they must be parallel to each other.Let the slopes of the lines be $m_1$ and $m_2$.For the first l

Vedclass · Accepted Answer

exactly one value of $p$

Vedclass · Answer

(A) If two lines are perpendicular to a common line,they must be parallel to each other.Let the slopes of the lines be $m_1$ and $m_2$.For the first line $p(p^2 + 1)x - y + q = 0$,the slope $m_1 = \frac{p(p^2 + 1)}{1} = p(p^2 + 1)$.For the second line $(p^2 + 1)^2x + (p^2 + 1)y + 2q = 0$,the slope $m_2 = -\frac{(p^2 + 1)^2}{p^2 + 1} = -(p^2 + 1)$.Since the lines are parallel,$m_1 = m_2$.$p(p^2 + 1) = -(p^2 + 1)$.Since $p^2 + 1 
eq 0$ for any real $p$,we can divide by $(p^2 + 1)$.$p = -1$.Thus,there is exactly one value of $p$.

The lines $p(p^2 + 1)x - y + q = 0$ and $(p^2 + 1)^2x + (p^2 + 1)y + 2q = 0$ are perpendicular to a common line for :

Similar Questions

Consider the two curves $y = 2x$ and $x^2 - xy + 2y^2 = 28$. The absolute value of the tangent of the angle between the two curves at the points where they meet is:

If $S_1$ and $S_2$ are two straight lines such that the reflection of $S_1$ in $S_2$ and the reflection of $S_2$ in $S_1$ coincide,the angle between $S_1$ and $S_2$ is equal to?

If the lines $mx + 2y + 1 = 0$ and $2x + 3y + 5 = 0$ are perpendicular to each other,then what is the value of $m$?

Consider the straight lines:
$L_1 : x - y = 1$
$L_2 : x + y = 1$
$L_3 : 2x + 2y = 5$
$L_4 : 2x - 2y = 7$
The correct statement is:

Find the acute angle between the lines $y = 3$ and $y = \sqrt{3}x + 9$. (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module