The acute angle between the lines 6x^2 + 11xy | vedclass

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

Question

(B) The acute 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|

Vedclass · Accepted Answer

$	an^{-1}\left(\frac{\sqrt{361}}{4}ight)$

Vedclass · Answer

(B) The acute 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|$.Comparing the given equation $6x^2 + 11xy - 10y^2 = 0$ with $ax^2 + 2hxy + by^2 = 0$,we get $a = 6$,$b = -10$,and $2h = 11$,so $h = \frac{11}{2}$.Substituting these values into the formula:$	an 	heta = \left|\frac{2\sqrt{(\frac{11}{2})^2 - (6)(-10)}}{6 - 10}ight|$$	an 	heta = \left|\frac{2\sqrt{\frac{121}{4} + 60}}{-4}ight|$$	an 	heta = \left|\frac{2\sqrt{\frac{121 + 240}{4}}}{-4}ight| = \left|\frac{2 \cdot \frac{\sqrt{361}}{2}}{-4}ight| = \left|\frac{\sqrt{361}}{-4}ight| = \frac{\sqrt{361}}{4}$.Therefore,$	heta = 	an^{-1}\left(\frac{\sqrt{361}}{4}ight)$.

The acute angle between the lines $6x^2 + 11xy - 10y^2 = 0$ is

Similar Questions

The organization of living organisms starts with which level?

Acetaldehyde forms a white crystalline precipitate on mixing with a ...... solution of

$A$ Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is

Observe the following statements:
$I$. If $dy + 2xy dx = 2e^{-x^2} dx$,then $ye^{x^2} = 2x + c$.
$II$. If $ye^{-x^2} - 2x = c$,then $dx = (2e^{-x^2} - 2xy) dy$.
Which of the following is a correct statement?

The principle of immunization or vaccination is based on the property of ...........

Vedclass Test Series

Exam Paper Generator

Online Exam Module