Simultaneous equation help (1 Viewer)

[nrlwinner]

I need help with this question.

For what value of c is the line y=2x+c a tangent to the parabola y=x^2 -x -2

 

[study-freak]

 

[nrlwinner]

Thanks mate. I got another one here.

For what values of c is the line y=x+c a tangent to the circle x^2 + y^2 = 4?

Find the coordinates of the point of contact



I have already found that c = plus or minus 2 root 2

But I'm not sure how to find the coordinates.

 

[study-freak]

 

[jet]

Continuing on from there. You have two separate quadratics.
x² + 2sqrt{2} + 2 = 0
(x + sqrt{2})^2 = 0
x = -sqrt{2}
Similarly, from the other quadratic, x = sqrt{2}
x = sqrt{2}, y = -3sqrt{2}
x = -sqrt{2} y = +3sqrt{2}.
The reason they are reversed is because of the plus/minus.
Really you should say that c = 2sqrt(2) OR c = -2sqrt(2) and then work off each case. Then it wouldnt be so confusing.