Question

find the measures of the acute angle between the lines represented by x square +xy =0​

Answer 1

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given:

${x}^{2} + xy = 0$

To find: Find the measures of the acute angle between the lines.

Solution:

Tip: Compare the equation by standard equation

$\bold{a {x}^{2} + 2hxy + b {y}^{2} = 0}$

the acute angle between both lines

$\bold{\red{tan \theta = \left | \frac{2 \sqrt{ {h}^{2} - ab} }{a + b} \right| }}$

Step 1: Compare the given equation with standard equation and write coefficients.

$a = 1 \\ 2h = 1 \\ b = 0$

Step 2: Put the coefficients in formula

$tan \theta = \left | \frac{2 \sqrt{ { (\frac{1}{2} })^{2} - (1)(0)} }{1 + 0}\right |$

or

$tan \theta = \left | \frac{2 \sqrt{ (\frac{1}{2} })^{2} }{1}\right |$

or

$tan \theta = \left|2 \times \frac{1}{2} \right|$

or

$tan \theta = 1$

or

$\theta = {tan}^{ - 1} (1)$

or

$\theta = \frac{\pi}{4}$

Final answer:

Acute angle between the lines represented by x²+xy =0 is $\bold{\red{\theta = \frac{\pi}{4} }}$

Hope it helps you.

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