CONICS QUESTION HELP (1 Viewer)

[lonelynight99]

Find the equation of four tangent common to the hyperbola x^2 - 2 y^2 = 4 and the
Circle x^2 + y^2 = 1. Find the points of contact of these tangent
With the circle. Hint: let xx1 + yy1 = 1 be a tangent to x^2 + y^2 = 1 at
P (x1, y1)



I try this but it seem so confusing, I wonder if anyone can help me with it . Thanks in advance.

 

[Carrotsticks]

I'll get you started by finding the points. Let me know if you need more help and I'll finish it tomorrow (or today since it's 2:21am!):

 

[Carrotsticks]

Oh and a small typo with the last 4 points:

The first of the 4 should read (x_1,y_1) not (x_1,x_1)

 

[lonelynight99]

Ok I will try in the morning. Thanks bro really appreciate it

 

[lonelynight99]

I think on the second line the equation should be x^2 + y^2 = 1 right?
Instead of x^2 + y^2 = 4

 

[lonelynight99]

And how do u get from y_1^4 + y_1^2 - x_1^2 y_1^ 2 to y_1^2 - x_1^2 = 0