Question

Find the value of b, if the angle between the
lines given by 6x² + xy + by2 = 0 is 45°.
.​

Answer 1

Answer:

If the equation x2 + 5xy + 4y2 + 3x + 2y + c = 0 represents a pair of lines, then find the value of c and also the angle between the lines.Read more on Sarthaks.com - https://www.sarthaks.com/509682/if-the-equation-x-2-5xy-4y-2-3x-2y-c-0-represents-a-pair-of-lines-then-find-the-value-of-c-and-also

Answer 2

Answer:

The value of b is either -1 or -35

Step-by-step explanation:

The given pair of straight lines is $6x^{2} +xy+by^{2}=0$

Also given,the angle between these pair of straight lines is 45*

We know that for a pair of straight lines of the form $ax^{2} +2hxy+by^{2}=0$,the angle between the lines is given as

$Tan\theta=|\frac{2\sqrt{h^{2}-ab} }{a+b} |$

Comparing our given equation of pair of straight lines with $ax^{2} +2hxy+by^{2}=0$,we get $a=6\\h=\frac{1}{2}$

Substituting these values in the angle relation we get,

$tan45=\frac{2\sqrt{(\frac{1}{2})^{ 2}-6b} }{6+b} \\= > 1=\frac{2\sqrt{(\frac{1}{2})^{ 2}-6b} }{6+b}= > 6+b=2\sqrt{\frac{1}{4} -6b}$

Squaring on both sides we get

$(6+b)^{2}=4(\frac{1}{4} -6b)= > 36+b^{2}+12b=1-24b\\= > b^{2}+36b+35+0\\= > b=-1,-35$

Therefore,The value of b is either -1 or -35

#SPJ3