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Question

The angle between the lines is x2-xy-6y2-7x+31y-18=0


A

45°

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B

60°

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C

90°

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D

30°

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Solution

The correct option is A

45°


Explanation for the correct option:

Finding the angle between the lines,

Given the equation of circle is

x2-xy-6y2-7x+31y-18=01

We know that the general equation of circle is,

ax2+2hxy+by2+2gx+2fxy+c=02

Now, comparing the equations 1 and 2 we get,

a=1,b=-6,h=-12

Finding the angle between the two lines of equation using the formula,

tanθ=2h2-aba+b

Substitute the values of a=1,b=-6,h=-12 to find the angle
tanθ=2-122-(1)(-6)1+(-6)=214+61-6=2(1+24)4-5=2254-5=2(52)-5=2-5×52=|-1|tanθ=1or-1
By taking only the positive value of tanθ, we get

tanθ=1θ=tan-1(1)θ=45°

Therefore, the angle between the two lines is 45°.

Hence, option (A) is the correct answer.


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