11th Business Maths Monthly Test - 4 ( Analytical Geometry )

MABS Institution

11th Business Maths Monthly Test - 4 ( Analytical Geometry )-Aug 2020

Time : 2.00 Hours

Part - A

Generic 5 - Answer All Question

Find the value of p for which the straight lines 8px+(2-3p)y+1 = 0 and px +8y -7 =0 are perpendicular to each other.

Find the co-ordinated of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola
i) y² = 20x
ii) x² = 8y
iii) x² = -16y

Find the equation of the parabola whose focus is (1,3) and whose directrix is x-y+2=0.

Prove that the tangents to the circle x²+y²=169 at (5,12) and (12,-5) are perpendicular to each other.

Find the equation of the parabola whose focus is the point F(-1, -2) and the directrix is the line 4x - 3y + 2 = 0

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

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 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.

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 2x²+7xy+3y²+5x+5y+2=0 represent two straight lines and find their separate equations.

Find the equation of the circle passing through the points (0,0), (1, 2) and (2,0).

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

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11th Business Maths Monthly Test - 4 ( Analytical Geometry )

MABS Institution

11th Business Maths Monthly Test - 4 ( Analytical Geometry )-Aug 2020

Part - A

Generic 5 - Answer All Question

Find the value of p for which the straight lines 8px+(2-3p)y+1 = 0 and px +8y -7 =0 are perpendicular to each other.

Find the co-ordinated of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola i) y2 = 20x ii) x2 = 8y iii) x2 = -16y

Find the equation of the parabola whose focus is (1,3) and whose directrix is x-y+2=0.

Prove that the tangents to the circle x2+y2=169 at (5,12) and (12,-5) are perpendicular to each other.

Find the equation of the parabola whose focus is the point F(-1, -2) and the directrix is the line 4x - 3y + 2 = 0

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

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 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.

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 2x2+7xy+3y2+5x+5y+2=0 represent two straight lines and find their separate equations.

Find the equation of the circle passing through the points (0,0), (1, 2) and (2,0).

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

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Other Study material

11th Business Maths Weekly Test - 4 ( Trigonometry

11th Business Maths Monthly Test - 1 ( Trigonometr

11th Business Maths Monthly Test - 2 ( Trigonometr

11th Business Maths Monthly Test - 3 ( Trigonometr

11th Business Maths Monthly Test - 4 ( Trigonometr

11th Business Maths Weekly Test - 1 ( Differential

11th Business Maths Weekly Test -2 ( Differential

11th Business Maths Weekly Test - 3 ( Differentia

11th Business Maths Weekly Test - 4 ( Differential

11th Business Maths Monthly Test - 1 ( Differentia

11th Business Maths Monthly Test - 2 ( Differentia

11th Business Maths Monthly Test - 3 ( Differentia

11th Business Maths Monthly Test - 4 ( Differentia

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11th Business Maths Weekly Test - 2 ( Applications

Tamilnadu Stateboardszs - Class

Find the co-ordinated of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola
i) y² = 20x
ii) x² = 8y
iii) x² = -16y

Prove that the tangents to the circle x²+y²=169 at (5,12) and (12,-5) are perpendicular to each other.

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.

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 2x²+7xy+3y²+5x+5y+2=0 represent two straight lines and find their separate equations.

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