2nd Year Mathematics Chapter 7 Test07: Conic Section

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

1. The focus of the parabola x²= − 16y is:
   1. (4 , 0)
   2. (– 4 , 0)
   3. (0 , 4)
   4. (0 , – 4)
2. Equation of conjugate axis of the hyperbola $\frac{(x-1)^2}{4} - \frac{(y+3)^2}{12} = 1 \text{ is:}$
   1. x = 1
   2. x = - 1
   3. y = 3
   4. y = - 3
3. $\text{The chord joining the two points } (at_1^2, 2at_1) \text{ and } (at_2^2, 2at_2) \text{ on the parabola } y^2 = 4ax \text{ is focal chord if:}$
   1. $$t_1 + t_2 = 1$$
   2. $$t_1 + t_2 = -1$$
   3. $$t_1 t_2 = 1$$
   4. $$t_1 t_2 = -1$$
4. Exactly one tangent can be drawn to a circle if point lies:
   1. Outside the circle
   2. On the circle
   3. Inside the circle
   4. Centre of circle
5. Length of the tangent drawn from the point (1 , 2) to the circle 2x² + 2y² + 3x + 2y - 6 = 0 is
   1. 11
   2. $\sqrt{11}$
   3. $\frac{11}{2}$
   4. $\sqrt{\frac{11}{2}}$
6. Eccentricity of the hyperbola $\frac{x^2}{25} - \frac{y^2}{81} = 1 \text{ is:}$
   1. $\frac{5}{\sqrt{106}}$
   2. $\frac{\sqrt{106}}{5}$
   3. $\frac{\sqrt{106}}{9}$
   4. $\frac{9}{\sqrt{106}}$
7. Length of the latus rectum of the ellipse $\frac{x^2}{16} +\frac{y^2}{9} = 1 \text{ is:}$
   1. $\frac{32}{9}$
   2. $\frac{9}{32}$
   3. $\frac{9}{2}$
   4. $\frac{8}{9}$
8. The eccentricity is the ratio of distance of a point on the conic section from:
   1. Focus to directrix
   2. Directrix to focus
   3. Vertex to directrix
   4. Directrix to vertex
9. Eccentricity of circle is:
   1. e > 1
   2. e < 1
   3. e = 1
   4. e = 0
10. $\text{Equation of the directrices of ellipse } \frac{x^2}{16} + \frac{y^2}{36} = 1 \text{ is:}$
    1. $y = \pm\frac{18}{\sqrt{5}}$
    2. $y = \pm\frac{\sqrt{5}}{18}$
    3. $y = \frac{18}{\sqrt{5}}$
    4. $y = \frac{\sqrt{5}}{18}$