1. The angle between the asymptotes of to $\frac{x^2}{a^2}\frac{y^2}{b^2}$=1 is equal to

2. The equation of a tangent parallel to y = x drawn to $\frac{x^2}{3}$-$\frac{y^2}{2}$=1 is

3. The equation $\frac{x^2}{12-k}$+$\frac{y^2}{8-k}$ = 1 represents

4. The equation a$x^2$ + 2hxy + b$y^2$ + 2gx + 2fy + c = 0 represents a rectangular hyperbola if

5. The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci, is

6. The eccentricity of the ellipse represented by the equation 25$x^2$ + 16$y^2$ - 150x - 175 = 0 is

7. The equation $\frac{x^2}{10-a}$+$\frac{y^2}{4-a}$=1 represents an ellipse, if

8. The eccentricity of an ellipse $\frac{x^2}{a^2}$+$\frac{y^2}{b^2}$=1, whose latus rectum is half of its minor axis is

9. If A and B are two fixed points and P is a variable point such that PA + PB = 4, the locus of P is

10. The eccentric angle of a point on the ellipse $\frac{x^2}{6}$+$\frac{y^2}{2}$=1 whose distance from the centre of the ellipse is 2, is

11. If the line x + y - 1 = 0 touches the parabola $y^2$ = kx, then the value of k is

12. If y = mx + c touches the parabola $y^2$ = 4a (x + a), then

13. The cordinates of a point on the parabola $y^2$ = 8x whose focal distance is 4, are

14. The equation of the directix of the parabola $x^2$ - 4x - 3y + 10 = 0 is

15. The equation of a parabola having focus (-3, 0) and directrix x = 3 is

16. Equation of the circle which touches 3x + 4y = 7 and passes through (1, -2) and (4, -3) is

17. One of the diameters of the circle $x^2$ + $y^2$ - 12x + 4y + 6 = 0 is given by

18. Four distinct points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle for

19. The equation 2$x^2$ + 2hxy + b$y^2$ + 2gx + 2fy + c = 0 represents a circle, the condition will be

20. The circle $x^2$ + $y^2$ + 4x - 7y + 12 = 0 cuts an intercept on y-axis of length