Posted by **karan** on Saturday, March 2, 2013 at 5:08am.

find k if one of the lines given by kx^2+10xy+8y^2=0 is perpendicular to 2x-y=5

- geometry -
**Reiny**, Saturday, March 2, 2013 at 8:09am
The slope of 2x-y=5 is 2

So the slope of a perpendicular line is -1/2

kx^2 + 10xy + 8y^2 = 0 is supposed to be the intersection of 2 straight lines, so let's solve it for y

y = (-10x ± √(100x^2 - 32kx^2) )/16

= (-10x ± x√100-68k)/16

= x(-10 ± √(100-32k) )/16

So the slope of the two lines is (-10 ± √(100-32k) )/16

thus:

(-10 ± √(100-32k) )/16 = -1/2

-20 ± 2√100-32k = -16

±2√100-32k = 4

±√100-32k = 2

square both sides

100-32k = 4

32k=96

k=3

check my arithmetic.

## Answer This Question

## Related Questions

- geometry - Martin drew a pair of perpendicular lines and a pair of parallel ...
- Plz Check My Geometry - Out of 30 questions these few I struggled with. I put ...
- Plz Check My Geometry - Out of 30 questions these few I struggled with. I put ...
- Plz Check my Geometry(sOo0n) - 1.) Given points A(-4, 5), B(2, 3), C(0, 4) and D...
- Geometry - Prove that the tangents to a circle at the endpoints of a diameter ...
- geometry - find the slope of a line that passes through the following points. (4...
- geometry - Create a wrapping paper design that includes at least four of the ...
- Geometry cheak - Choose whether the lines given below are parallel, ...
- Math! Please check! - Given that lines AC and GE are both perpendicular to line ...
- Analytic Geometry - Reflecting points over lines - Let P = (5,1), and let Q be ...

More Related Questions