Question

The distance between the pair of parallel lines represented by the expression x2 + 2xy + y2 - 8ax - 8ay - 9a2 = 0 is

Answer 1

In the attachment I have answered this problem.

The given equation is factorized to find the separate equations of the parallel lines.

The distance is calculated by applying suitable formula.

I hope this answer help you

Answer 2

The complete question is:

If the distance between the pair of parallel lines represented by the expression x^2 + 2xy + y^2 - 8ax - 8ay - 9a^2 = 0 is s 25 $\sqrt{2}$, then a is:

Answer:

The value of a is ±5.

Explanation:

The equation,

ax^2 + hxy + by^2 + 2gx + 2fy + c = 0

displays the general equation of two lines being ║to one another. Thus, the distance among them would be calculated by:

d = |$2\sqrt{\frac{g^{2} - ac }{a(a + b)} }$| or d = | $2\sqrt{\frac{f^{2} - ac }{b(a + b)} }$|

The given equation is:

x^2 + 2xy + y^2 - 8ax - 8ay - 9a^2 = 0

so, a = 1, b = 1, c = -9a^2, h = 1, f = -4a, g = -4a

Thus, d = 25 $\sqrt{2}$

⇒ 25 $\sqrt{2}$ = | 2 $\sqrt{\frac{(-4a^{2}) - 1 (-9a^{2}) }{1 (1 + 1)} }$|

⇒ 25 $\sqrt{2}$ = $\sqrt{2}$(5a)

⇒ a = ±5

∵ The value of a is ±5.

Learn more: parallel expression

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