If theta is the angle between the lines x^2+2 | vedclass

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

Question

(A) The angle $	heta$ between the pair of lines $ax^2 + 2hxy + by^2 = 0$ is given by $	an 	heta = \left| \frac{2\sqrt{h^2 - ab}}{a+b} ight|$.For

Vedclass · Accepted Answer

$	heta$

Vedclass · Answer

(A) The angle $	heta$ between the pair of lines $ax^2 + 2hxy + by^2 = 0$ is given by $	an 	heta = \left| \frac{2\sqrt{h^2 - ab}}{a+b} ight|$.For the first equation $x^2 + 2hxy + by^2 = 0$,the angle is $	heta$.For the second equation $x^2 + 2xy \sec 	heta + y^2 = 0$,we have $a=1$,$h=\sec 	heta$,and $b=1$.Let $\phi$ be the angle between these lines.Then $	an \phi = \left| \frac{2\sqrt{(\sec 	heta)^2 - (1)(1)}}{1+1} ight|$.$	an \phi = \left| \frac{2\sqrt{\sec^2 	heta - 1}}{2} ight|$.Since $\sec^2 	heta - 1 = 	an^2 	heta$,we have $	an \phi = \sqrt{	an^2 	heta} = |	an 	heta|$.Therefore,$\phi = 	heta$.

If $\theta$ is the angle between the lines $x^2+2 h x y+b y^2=0$,then the angle between $x^2+2 x y \sec \theta+y^2=0$ is

Similar Questions

$6 \Omega$ and $12 \Omega$ resistors are connected in parallel. This combination is connected in series with a $10 \text{ V}$ battery and a $6 \Omega$ resistor. What is the potential difference between the terminals of the $12 \Omega$ resistor (in $text{ V}$)?

Which of the following pairs is mismatched?

If the lines $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+\lambda y-8=0$ are concurrent,then $\lambda$ equals

Which reagent is used to remove $SO_4^{2-}$ and $Cl^{-}$ ions from a solution?

$A$ satellite is launched into a circular orbit of radius $R$ around the Earth,while a second satellite is launched into an orbit of radius $1.02 R$. The percentage difference in the time periods of the two satellites is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module