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...