11th Maths Weekly Test 4 ( Two Dimensional Analytical Geometry)

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test 4 ( Two Dimensional Analytical Geometry)-Aug 2020

Time : 1.30 Hours

Part - A

Generic 3 - Answer All Question

If one of the straight lines of ax² + 2hxy + by² = 0 is perpendicular to px + qy = 0, then show ap²+2hpq+bp²=0

Find the equation of the line which passes through the point (- 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5: 3 by this point.

A straight rod of the length 6 units, slides with its ends A and B always on the x and y axes respectively. If O is the origin, then find the locus of the centroid of ΔOAB.

Find the equation to the bisectors of the angle between 5x+12y-7=0 and 4x-3y+1=0

Show the points \((0,-\frac{3}{2}),(1,-1)\) and \((2,-\frac{1}{2})\) are collinear.

If θ is a parameter, find the equation of the locus of a moving point, whose coordinates are (a(θ-sinθ),a(1-cosθ)).

If R is any point on the x - axis and Q is any point on the y- axis and P is a variable point on RQ with RP = b, PQ = a. then find the equation of locus of P

Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120^o with the positive direction of x-axis.

Show that the equation 9x² -24xy +16y² +12x + 16y -12 = 0 represents a pair parallel lines. find the distance between them

Find the nearest point on the line 2x +y = 5 from the origin.

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11th Maths Weekly Test 4 ( Two Dimensional Analytical Geometry)

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test 4 ( Two Dimensional Analytical Geometry)-Aug 2020

Part - A

Generic 3 - Answer All Question

If one of the straight lines of ax2 + 2hxy + by2 = 0 is perpendicular to px + qy = 0, then show ap2+2hpq+bp2=0

Find the equation of the line which passes through the point (- 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5: 3 by this point.

A straight rod of the length 6 units, slides with its ends A and B always on the x and y axes respectively. If O is the origin, then find the locus of the centroid of ΔOAB.

Find the equation to the bisectors of the angle between 5x+12y-7=0 and 4x-3y+1=0

Show the points \((0,-\frac{3}{2}),(1,-1)\) and \((2,-\frac{1}{2})\) are collinear.

If θ is a parameter, find the equation of the locus of a moving point, whose coordinates are (a(θ-sinθ),a(1-cosθ)).

If R is any point on the x - axis and Q is any point on the y- axis and P is a variable point on RQ with RP = b, PQ = a. then find the equation of locus of P

Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120o with the positive direction of x-axis.

Show that the equation 9x2 -24xy +16y2 +12x + 16y -12 = 0 represents a pair parallel lines. find the distance between them

Find the nearest point on the line 2x +y = 5 from the origin.

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If one of the straight lines of ax² + 2hxy + by² = 0 is perpendicular to px + qy = 0, then show ap²+2hpq+bp²=0

Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120^o with the positive direction of x-axis.

Show that the equation 9x² -24xy +16y² +12x + 16y -12 = 0 represents a pair parallel lines. find the distance between them