SOLUTION: Find value(s) of k such that y=kx-3 is tangent to the parabola y=2x^2+ 10

Question 1181587: Find value(s) of k such that y=kx-3 is tangent to the parabola y=2x^2+ 10
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
Find value(s) of k such that y=kx-3 is tangent to the parabola y=2x^2+ 10

If you haven't had calculus, then we do it this way:

A line is tangent to a parabola if and only if the assumption of their
equations holding true leads to a single solution with multiplicity 2.

We substitute (kx-3) for y in 






This will have a single solution with multiplicity 2 if its discriminant
equals 0.








Those are the two and the only such values of k.

Edwin

RELATED QUESTIONS
If the graph of the parabola y=kx^2+6x+k+8 is tangent to x-axis, then what is the... (answered by oscargut)

for what value(s) of k is the line 2x=3y+k a tangent to the parabola... (answered by stanbon)

For what value of k the line 2x-y+k=0 is tangent to the parabola... (answered by josgarithmetic,ikleyn,Alan3354)

Find all k so that the graph of y = -1/4x^2 +kx -9 is tangent to the... (answered by Alan3354)

Given y = −3x^2 + kx − 12 for k > 0, find the value(s) of k such that y < 0 for all... (answered by MathLover1,ikleyn)

Find the value of k for which y=kx-2 is a tangent to the curve... (answered by ikleyn,greenestamps)

The line y=k is a tangent to the parabola y= x^2 -8x +18. a) show this on a diagram... (answered by josgarithmetic)

Find the value for c such that y = x + c is a tangent to the parabola y = x^2-x-12.... (answered by josgarithmetic)

Find the value(s) of k such that the graph of the equation k(x^2+y^2 )+x^2-y^2+x+y=0 is (answered by josgarithmetic)