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## #1 2008-01-07 01:18:23

ganesh
Moderator

Online

### Pre-University - IV

1. Solve by Cramer's rule:- x+y=1, y+z=1, z+x=4.

2. Solve by Cramer's rule:- 3x+y+z=3, 2x+2y+5z+1 = 0, x-3y-4z=2.

3. Solve using Cramer's Rule:- 2/x+3/y+1/z=4; 4/x-6/y+3/z=-7; 3/x-5/y+2/z=-5.

4. Find the equations of the two tangents that can be drawn from the point (1, -2) to the parabola y² = 3x.

5. Find the two tangents that can be drawn from (3,4) to the parabola y² = 4x.

6. Find the condition for the straight line y=mx+c to be a tangent to the ellipse

7. Find the center, vertices, foci, eccentricity, latus rectum and directrices of the
hyperbola 12x²-4y²-24x+32y-127=0.

8. Find the asymptotes of the hyperbola 8x²+10xy-3y²-2x+4y-2 = 0.

9. Find the center, eccentricity, foci, directrices, and latus rectum of the ellipse
3x²+4y²-12x-8y+4 = 0.

10. Find the equation of the asymptotes of the rectangular hyperbola
6x²+5xy-6y²+12x+5y+16 = 0.

11. Find the eccentricity, length of latus rectum, center, foci, and equations of directrices of the ellipse 3x²+4y²-6x+8y-5 = 0.

12. Find the equation of the rectangular hyperbola with center (-1,3) which has one of its asymptotes the line x+2y-5= 0 and passes through the point (3,-2).

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