Saved Bookmarks
| 1. |
The contact point of the line y = x-2 with the ellipse 3x2 + 4y2 = 24 is A. (-4,3)B. (4,-3)C.(4,3)D. None of these |
|
Answer» Put \(y=x-2 \,in \,eqquation\, of \,ellipse\) \(3x^2+4y^2=24\) we obtain \(3x^2+4(x-2)^2=24\) \(=3x^2+4x^2-16x+16=24\) \(=7x^2-16x-8=0\) \(=x=\frac{16\pm \sqrt{256+224}}{14}\) \(x=\frac{16\pm \sqrt{480}}{14}=\frac{8\pm2\sqrt{30}}{7}\) \(y=\frac{8+2\sqrt{30}}{7}-2\,or\,y=\frac{8-2\sqrt{30}}{7}-2\) \(=y=\frac{2\sqrt{30}-6}{7}\,or\,y=\frac{-2\sqrt{30}-6}{7}\) But line y = x - 2 intersects ellipse not touching it Hence option (D) is corret for line y = x-2. |
|