Maths Whizz
Math whizz please help me!!!?
1) find the value of p for which the x-axiz is a tangent to the curve y= x^2 + px – p + 3. For each of the values, find the coordinates of the points of tangency. i have solved for p which is p = 2 and p= – 6. So how to find the coordinates??
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(2) If the curve y = kx(x +2) meets the line y = x – k, find the range of values k. State the value of k for which the line is a tangent.
1/ you are right that
p=2 and p=-6
To find the x coordinate solve
0=x^2+px-p+3 for p=2
and for p=-6 and you find
x=-1 and x=3
so the points are (-1,0) (3,0)
2/You have the system
y=kx^2+2kx
y=x-k
By substitution you take
kx^2+2kx=x-k
kx^2+(2k-1)x+k=0
that must have a real solution
D>=0 and k=/0 (k not 0)
(2k-1)^2-4k^2>=0
4k^2-4k+1-4k^2>=0
4k<=1 , k<=1/4 and k=/0
When k=1/4 line is tangent
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