marsenal
cHeAp bOoKs
- Joined
- Nov 12, 2002
- Messages
- 273
From Patel's blue book:
1.Show that the line lx+my+n=0 touches the
(a)ellipse x<sup>2</sup>/a<sup>2</sup> + y<sup>2</sup>/b<sup>2</sup>=1, if a<sup>2</sup>l<sup>2</sup> + b<sup>2</sup>m<sup>2</sup>=n<sup>2</sup>
(b) hyperbola x<sup>2</sup>/a<sup>2</sup>-y<sup>2</sup>/b<sup>2</sup>=1, if a<sup>2</sup>l<sup>2</sup>-b<sup>2</sup>m<sup>2</sup>=n<sup>2</sup>
2.The tangent at P(x<sub>1</sub>,y<sub>1</sub>) on the hyperbola x<sup>2</sup>/a<sup>2</sup>-y<sup>2</sup>/b<sup>2</sup>=1, x<sub>1</sub> >1, intersects the directorix at Q. S is the focus (ae,0). Prove that PSQ is a right angle.
3. Find the equations of the four tangents common to the hyperbola x<sup>2</sup>-2y<sup>2</sup>=4 and the circle x<sup>2</sup>+y<sup>2</sup>=1. Find the points of contact of these tangents with the circle.
Thanx!
1.Show that the line lx+my+n=0 touches the
(a)ellipse x<sup>2</sup>/a<sup>2</sup> + y<sup>2</sup>/b<sup>2</sup>=1, if a<sup>2</sup>l<sup>2</sup> + b<sup>2</sup>m<sup>2</sup>=n<sup>2</sup>
(b) hyperbola x<sup>2</sup>/a<sup>2</sup>-y<sup>2</sup>/b<sup>2</sup>=1, if a<sup>2</sup>l<sup>2</sup>-b<sup>2</sup>m<sup>2</sup>=n<sup>2</sup>
2.The tangent at P(x<sub>1</sub>,y<sub>1</sub>) on the hyperbola x<sup>2</sup>/a<sup>2</sup>-y<sup>2</sup>/b<sup>2</sup>=1, x<sub>1</sub> >1, intersects the directorix at Q. S is the focus (ae,0). Prove that PSQ is a right angle.
3. Find the equations of the four tangents common to the hyperbola x<sup>2</sup>-2y<sup>2</sup>=4 and the circle x<sup>2</sup>+y<sup>2</sup>=1. Find the points of contact of these tangents with the circle.
Thanx!
