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11th Business Maths Monthly Test - 2 ( Analytical Geometry )

MABS Institution

11th Business Maths Monthly Test - 2 ( Analytical Geometry )-Aug 2020

Time : 2.30 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 distance between directrix and focus of a parabola y² = 4ax is

a
2a
4a
3a

The locus of the point P which moves such that P is always at equidistance from the line x + 2y+ 7 = 0 is

x+2y+2=0
x - 2y + 1 = 0
2x - y + 2 = 0
3x + y + 1=0

If m₁ and m₂ are the slopes of the pair of lines given by ax²+ 2hxy + by² = 0, then the value of m₁+ m₂ is

2h/b
-2h/b
2h/a
-2h/a

The focus of the parabola x² = 16y is

(4,0)
(-4,0)
(0,4)
(0,-4)

If the perimeter of the circle is 8π units and centre is (2,2) then the equation of the circle is

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

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

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

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 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 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

Part - B

Generic 2 - Answer All Question

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

If the angle between the two lines is \(\frac{\pi}{4}\) and slope of one of the lines is 3, then find the slope of the other line.

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

If the lines 3x-5y-11=0, 5x+3y-7=0 and x+ky=0 are concurrent, find the value of k.

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

Find the equation of the circle having (4,7) and (-2,5) as the extremities of a diameter

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

Part - C

Generic 3 - Answer All Question

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

Find the condition that the straight lines y=m₁x+C₁_,y=m₂x+C₂, and y=m₃x+C₃ may meet at a point?

Find the values of a and b if the equation (a-1)x²+by²+(b-8) xy+4x+4y-1=0 represents a circle.

For what value of k does 12x²+7xy+ky²+13x-y+3=0 represents a pair of straight lines?

The slope of one of the straight lines ax²+2hxy+by²=0 is twice that of the other, show that 8h²=9ab.

Find the locus of a point, so that the join of (–5, 1) and (3, 2) subtends a right angle at the moving point.

Find the combined equation of the straight line through the origin, one of which is parallel to and the other is perpendicular to the straight line 2x+y+1=0

Part - D

Generic 5 - Answer All Question

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

If the equation ax² +5xy -6y² +12x + 5y +c = 0 represents a pair of perpandicular straight lines, find a and c.

Show that the equation 12x² -10xy +2y² +14x -5y +2 = 0 represents a pair of straight lines also find the separate equations of the straight lines

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How side is 2 m from the vertex of the parabola?

Show that the point (7, –5) lies on the circle x²+y²-6x+4y-12=0 and find the coordinates of the other end of the diameter through this point.
Find the equation of the parabola whose vertex is (0, 0) passing through the point (2, 3) and axis is along X-axis.

Show that the pair of straight lines 4x² +12xy +9y² -6x -9y +2 = 0 represents two parallel straight lines and also find the separate equations of the straight lines..

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