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11th Business Maths Weekly Test - 1 ( Analytical Geometry )

MABS Institution

11th Business Maths Weekly Test - 1 ( Analytical Geometry )-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

(1, - 2) is the centre of the circle x²+ y² + ax + by - 4 = 0 , then its radius

3
2
4
1

The double ordinate passing through the focus is

focal chord
latus rectum
directrix
axis

ax² + 4xy + 2y² = 0 represents a pair of parallel lines then 'a' is

2
-2
4
-4

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

4
16
±4
±16

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

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

Combined equation of co-ordinate axes is

x²-y²=0
x²+y²=0
xy=c
xy=0

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

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

Length of the latus rectum of the parabola y² = - 25x is

25
-5
5
-25

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

a
2a
4a
3a

Part - B

Generic 2 - Answer All Question

Find the cartesian equation of the circle whose parametric equation are x = 3 cos\(\theta\), y = 3 sin\(\theta\) \(0\le \theta \le 2\pi \)

Convert the parabola y²=4x+4y into standard form.

Find the centre and radius of the circle x²+y²-8x+6y-24 = 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.

Part - C

Generic 3 - Answer All Question

Find the separate equations of the pair of lines given by 3x²+7xy+2y²+5x+5y+2=0.

Find the axis, vertex, focus, equation of directrix and length of latus rectum for the parabola x²+6x-4y+21=0

A manufacturer produces 80 TV sets at a cost of Rs. 2,20,000 and 125 TV sets at a cost of Rs. 2,87,500. Assuming the cost curve to be linear, find the linear expression of the given information. Also estimate the cost of 95 TV sets.
Determine whether the points p(1,0), Q(2,1) and R(2,3) lie outside the circle, on the ciircle or inside the circle x² + y² - 4x- 6y + 9 = 0

A point P moves so that P and the points (2,2) and(1,5) are always collinear. Find the locus of P.

Part - D

Generic 5 - Answer All Question

Show that the given lines 3x-4y-13=0, 8x-11y=33 and2x-3y-7=0 are concurrent and find the concurrent point.

Find the angle between the pair of straight lines 3x² -5xy -2y² +17x + y + 10 = 0

Find whether the points (-1,-2), (1,0) and (-3, -4) lie above, below or on the line 3x+2y+7 =0.

Find the axis, vertex, focus, equation of directrix length of latus rectum of the parabola (y-2)²=4(x-1).
As the number of units manufactured increases from 6000 to 8000, the total cost of production increases from Rs. 33,000 to Rs. 40,000. Find the relationship between the cost (y) and the number of units made (x) if the relationship is linear.

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