Value of 'k' for a Curve and a Line

[heleep]

"Find the values of k such that the straight line y=2x+k meets the curve with equation x²+2xy+2y²=5 exactly once."

So b² -4ac must equal 0 for one root, but how do I solve this with the 'xy' and 'y²' variables?

 

[Deleted member 4993]

"Find the values of k such that the straight line

y=2x+k .... (1) meets the curve with equation

x²+2xy+2y²=5 ..... (2)

exactly once."

So b² -4ac must equal 0 for one root, but how do I solve this with the 'xy' and 'y²' variables?

Replace 'y' in (2) by (1)

x^2 + 2x(2x+k) + 2(2x+k)^2 = 5 ..............edited

13x^2 + 10kx + 2k^2-5 = 0 .............. edited

Now continue....

 

[HallsofIvy]

The equation Subhotosh Kahn gave you is a quadratic equation. Do you remember the conditions under which such an equation will have one, two, or no real roots?

 

[heleep]

ahh, of course. I was making them equal each other instead of substituting. thanks.

...and yes, HallsofIvy. thanks.