#### 12th Standard Maths Two Dimensional Analytical Geometry-II English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021

12th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

Answer all the questions

10 x 1 = 10
1. The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is

(a)

$\frac { 4 }{ 3 }$

(b)

$\frac { 4 }{ \sqrt { 3 } }$

(c)

$\frac { 2 }{ \sqrt { 3 } }$

(d)

$\frac { 3 }{ 2 }$

2. The area of quadrilateral formed with foci of the hyperbolas $\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\\$ and $\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =-1$

(a)

4(a2+b2)

(b)

2(a2+b2)

(c)

a2 +b2

(d)

$\frac { 1 }{ 2 }$(a2+b2)

3. Tangents are drawn to the hyperbola  $\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1$ 1parallel to the straight line2x−y=1. One of the points of contact of tangents on the hyperbola is

(a)

$\frac { 9 }{ 2\sqrt { 2 } } ,\frac { -1 }{ \sqrt { 2 } }$

(b)

$\frac { -9 }{ 2\sqrt { 2 } } ,\frac { 1 }{ \sqrt { 2 } }$

(c)

$\frac { 9 }{ 2\sqrt { 2 } } ,\frac { 1 }{ \sqrt { 2 } }$

(d)

$\left( 3\sqrt { 3 } ,-2\sqrt { 2 } \right)$

4. Area of the greatest rectangle inscribed in the ellipse $\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1.$ is

(a)

2ab

(b)

ab

(c)

$\sqrt{ ab}$

(d)

$\frac { a }{ b }$

5. The values of m for which the line y=mx+ $2\sqrt { 5 }$ touches the hyperbola 16x2−9y2=144 are the roots of x2−(a+b)x−4=0, then the value of (a+b) is

(a)

2

(b)

4

(c)

0

(d)

-2

6. The equation of the directrix of the parabola y2+ 4y + 4x + 2 = 0 is

(a)

x = -1

(b)

x = 1

(c)

x = $\frac{-3}{2}$

(d)

x = $\frac{3}{2}$

7. If the distance between the foci is 2 and the distance between the direction is 5, then the equation of the ellipse is

(a)

6x2 + 10y2 = 5

(b)

6x2 + 10y2 = 15

(c)

x2 + 3y2 = 10

(d)

none

8. The length of major and minor axes of 4x2 + 3y2 = 12 are ____________

(a)

4, 2$\sqrt3$

(b)

2, $\sqrt3$

(c)

2$\sqrt3$, 4

(d)

$\sqrt3$, 2

9. The locus of the foot of perpendicular from the focus on any tangent to y2 = 4ax is

(a)

x2 + y2 = a2 - b2

(b)

x2 + y2 = a2

(c)

x2 + y2 = a2 - b2

(d)

x = 0

10. The locus of the point of intersection of perpendicular tangents of the parabola y2 = 4ax is

(a)

latus rectum

(b)

directrix

(c)

tangent at the vertex

(d)

axis of the parabola