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11th Business Maths Weekly Test - 3 ( Analytical Geometry )

MABS Institution

11th Business Maths Weekly Test - 3 ( Analytical Geometry )-Aug 2020

Time : 2.00 Hours

Part - A

Multiple Choice Question - Answer All Question

Combined equation of co-ordinate axes is

x²-y²=0
x²+y²=0
xy=c
xy=0

The centre of the circle x² + y - 2x + 2y - 9 = 0 is

(1,1)
(-1,-1)
(-1,1)
(1, -1)

The length of the tangent from (4,5) to the circle x² +y² = 16 is

4
5
16
25

The eccentricity of the parabola is

3
2
0
1

If kx² + 3xy - 2y²= 0 represent a pair of lines which are perpendicular then k is equal to

1/2
-1/2
2
-2

The distance between directrix and focus of a parabola y² = 4ax is

a
2a
4a
3a

The equation of the circle with centre (3,-4) and touches the x - axis

(x - 3)² +(y - 4)² = 4
(x - 3)² +(y + 4)² =16
(x-3)²+(y- 4)²=16
x²+y²=16

The angle between the pair of straight lines x² - 7xy + 4y² = 0

\(tan^{-1}\left(1\over 3\right)\)
\(tan^{-1}\left(1\over 2\right)\)
\(tan^{-1}\left(\sqrt{33}\over 5\right)\)
\(tan^{-1}\left(5\over\sqrt{33}\right)\)

The x - intercept of the straight line 3x + 2y - 1 = 0 is

3
2
1/3
1/2

The slope of the line 7x + 5y - 8 = 0 is

7/5
-7/5
5/7
-5/7

If the circle touches x axis, y axis and the line x = 6 then the length of the diameter of the circle is

6
3
12
4

The equation of the circle with centre on the x axis and passing through the origin is

x² - 2ax + y = 0
y² - 2ay + x² = 0
x²+y²=a²
x² - 2ay + y = 0

The equation of directrix of the parabola y² = - x is

4x+ 1 =0
4x - 1 = 0
x - 4=0
x + 4 = 0

If the centre of the circle is (-a, -b) and radius \(\sqrt{a^2-b^2}\)then the equation of circle is

x²+y²+2ax+2by+2b²=0
x²+y²+2ax +2by-2b²=0
x² +y² - 2ax - 2by - 2b² = 0
x² + y - 2ax - 2by + 2b² = 0

In the equation of the circle x² +y² = 16 then y-intercept is (are)

4
16
±4
±16

Part - B

Generic 2 - Answer All Question

Find the equation of the circle on the line joining the points (1,0), (0,1) and having its centre on the line x + y= 1

Find the center and radius of the circle x² + y² - 22x - 4y + 25 = 0

Find the equation of the circle with centre at (3, –1) and radius is 4 units.

Convert the equation of the parabola x²+y=6x-14 into the standard form.

Find the centre and radius of the circle x² + y² = 16

Find the equation of the following circles having the center ( 0,0) and radius 2 units

Find the center and radius of the circle (x + 2) ( x - 5) + (y -2 ) ( y -1) = 0

Show that perpendicular distances of the line x-y+5=0 from origin and from the point P(2, 2) are equal.

Find the equation of the following circles having the center (3,5) and radius 5 units

Find the equation of the circle with centre at origin and radius is 3 units.

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