conics (1 Viewer)

[c0okies]

hi; i feel very noob at conics.. can someone help me with these questions?

1. The chord joining the poitn alpha and beta on the ellipse with the equation x^2/a^2+y^2/b^2=1 subtends a right angle at the point (a,0). Show that tan(alpha/2)tan(beta/2)=-b^2/a^2

2. Show that the line 2y+x+5=0 is a tangent x^2/9+y^2/4=1. FInd the coordinates of the point of contact

 

[haboozin]

2. Show that the line 2y+x+5=0 is a tangent x^2/9+y^2/4=1. FInd the coordinates of the point of contact

2 is simple just solve simultaniously (easiest way is to substitute in the ellipse x = -2y-5

then show that this creates a perfect square, 1 answer thus its a tangent.
now that you know the y quadrant put it in the tangent and get the x quadrant.

 

[c0okies]

oh. oh ok thanx.. i'll try that =D