The angle between the lines represented by th | vedclass

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

Question

(A) The given equation is $x^2 - 2pxy + y^2 = 0$. Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we have $a = 1$,$h = -p$,and $b = 1$.L

Vedclass · Accepted Answer

$\sec^{-1} p$

Vedclass · Answer

(A) The given equation is $x^2 - 2pxy + y^2 = 0$. Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we have $a = 1$,$h = -p$,and $b = 1$.Let $	heta$ be the angle between the lines. The formula for the angle is $	an 	heta = \left| \frac{2\sqrt{h^2 - ab}}{a + b} ight|$.Substituting the values,$	an 	heta = \left| \frac{2\sqrt{(-p)^2 - (1)(1)}}{1 + 1} ight| = \left| \frac{2\sqrt{p^2 - 1}}{2} ight| = \sqrt{p^2 - 1}$.Since $	an 	heta = \sqrt{p^2 - 1}$,we have $\sec^2 	heta = 1 + 	an^2 	heta = 1 + (p^2 - 1) = p^2$.Thus,$\sec 	heta = p$,which implies $	heta = \sec^{-1} p$.

The angle between the lines represented by the equation $x^2 - 2pxy + y^2 = 0$ is

Similar Questions

The equation $x^2 - 3xy + \lambda y^2 + 3x - 5y + 2 = 0$,where $\lambda$ is a real number,represents a pair of straight lines. If $\theta$ is the angle between the lines,then $\text{cosec}^2 \theta =$

If the coordinate axes are the bisectors of the angles between the pair of lines $ax^2 + 2hxy + by^2 = 0$,where $h^2 > ab$ and $a \neq b$,then

The angle between the lines given by $x^2 - y^2 = 0$ is ..... $^o$.

If lines represented by the equation $px^2 - qy^2 = 0$ are distinct,then

If $\theta_1$ and $\theta_2$ are the acute angles between the pairs of lines $3x^2 - 7xy + 4y^2 = 0$ and $6x^2 - 5xy + y^2 = 0$ respectively,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module