Question

The length of x-intercept made by pair of lines
2x2 + xy - 6y2 - 2x + 17y - 12 = 0 is
2) 10 3) 5
4) 20
1) 2​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The length of x intercept made by pair of lines is

$5 \sqrt{2} \: units$

Step-by-step explanation:

Given that the pair of lines are

$\\ 2x {}^{2} + xy - 6y {}^{2} - 2x + 17y - 12 = 0$

Comparing this with the standard equation of pair of lines which is mentioned below

$\\ ax {}^{2} + by {}^{2} + 2hxy + 2gx + 2fy + c = 0$

we get the coefficients as

$a = 2 \: \\ b = - 6 \: \\ c = - 12 \: \\ g = - 1 \: \\ f = \frac{17}{2} \: \\ h = \frac{1}{2}$

The formula for length of x intercept made by the pair of lines is mentioned below

$l _{x} = 2 \sqrt{ \frac{g {}^{2} - ac }{ |a| } }$

Substituting the given coefficients,we get the length of x intercept as

$l _{x} = 2 \sqrt{ \frac{( - 1) {}^{2} - (2)( - 12) }{ |2| } } \\ = 2 \sqrt{ \frac{25}{2} } = 5 \sqrt{2} \: units$

Therefore,the length of x intercept formed by given pair of lines is

$5 \sqrt{2} \: units$

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