Question

If the slope of one line of 8x2 + 2hxy + y2 = 0 is double the other, then h?​

Answer 1

Answer:

This is the equation of the line so ,

$</p><p>(y−mx)(y−m2x)=0</p><p></p><p>m3x2−(m2+m)xy+y2=0</p><p></p><p>a=m3</p><p>h=−(2m2+m)</p><p>b=1</p><p>(ha+b)+(ab8h2)=−(m2(m2−m+1))+m2(m+1)2</p><p>(ha+b)+(ab8h2)=6</p><p></p><p>$

$=6</p><p></p><p></p><p>a2b+ab2−6abh+8h3=0</p><p></p><p></p><p></p><p>$

Step-by-step explanation:

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Answer 2

Answer:

The value of h is either 3 or -3

Step-by-step explanation:

The equation of pair of straight lines is given as

$8 {x}^{2} + 2hxy + {y}^{2} = 0$

It is formed by the pair of straight lines

$y - m_{1}x = 0 \: \\ y - m_{2}x = 0$

Given that one slope is twice the other.Therefore,

$m_{1} = 2m = > m_{2} = m$

Therefore,the equation of pair of straight lines become

$(y - 2mx)(y - mx) = 0 \\ = > {y}^{2} + 2{m}^{2} {x}^{2} - 3mxy = 0$

Comparing it with the given equation of pair kf straight lines,we get

$2 {m}^{2} = 8 \\ 2h = - 3m$

Hence,

$2 {m}^{2} = 8 = > {m}^{2} = \frac{8}{2} = 4 \\ = > m = ±2 \\ = > h = \frac{ - 3m}{2} = \frac{±6}{2} = ±3$

Therefore,The value of h is either 3 or -3

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