If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is two times the other, then
If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is two times the other, then
8h2 = 9ab
- 8h = 9ab
8h2 = 9ab2
8h = 9ab2
The Correct Option is A
Solution and Explanation
ax2 + 2hxy + by2 =0
m1 + m2 = -2h/b
m1m2 = \(\frac {a}{b}\)
Given:
m1 = 2m2
put m1 = 2m2
2m2 + m2 = \(\frac {- 2h}{b}\)
3m2 = \(\frac {- 2h}{b}\)
m2 = \(\frac {- 2h}{3b}\)
and 2m2 = \(\frac {a}{b}\)
m2 = \(\frac {a}{2b}\)
Now, \((\frac {- 2h}{3b})^2\) = \(\frac {a}{2b}\)
\(\frac {4h^2}{9b^2}\) = \(\frac {a}{2b}\)
8h2 = 9ab
Therefore the correct option is (A) 8h2 = 9ab
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Concepts Used:
The Slope of a Line
A slope of a line is the conversion in y coordinate w.r.t. the conversion in x coordinate.
The net change in the y-coordinate is demonstrated by Δy and the net change in the x-coordinate is demonstrated by Δx.
Hence, the change in y-coordinate w.r.t. the change in x-coordinate is given by,
\(m = \frac{\text{change in y}}{\text{change in x}} = \frac{Δy}{Δx}\)
Where, “m” is the slope of a line.
The slope of the line can also be shown by
\(tan θ = \frac{Δy}{Δx}\)
Read More: Slope Formula
The slope of a Line Equation:
The equation for the slope of a line and the points are known to be a point-slope form of the equation of a straight line is given by:
\(y-y_1=m(x-x_1)\)
As long as the slope-intercept form the equation of the line is given by:
\(y = mx + b\)
Where, b is the y-intercept.