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JEE Questions for Maths Rectangular Cartesian Coordinates Quiz 9 - MCQExams.com
JEE
Maths
Rectangular Cartesian Coordinates
Quiz 9
If O be the origin and if the co-ordinates of any two points Q
1
and Q
2
be (x
1
, y
1
) and (x
2
, y
2
) respectively. Then OQ
1
∙ OQ
2
cos Q
1
OQ
2
=
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x1 x2 – y1 y2
0%
x1 y1 – x2 y2
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x1 x2 + y1 y2
0%
x1 y2 + x2 y2
Given the points A(0,and B(0,4). Then the equation of the locus of the point P(x,y) such that |AP - BP) = 6 is
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0%
0%
2)
0%
0%
If ABCD is a quadrilateral, if the mid point of consecutive sides AB, BC, CD and DA are combined by straight lines, then the quadrilateral PQRS is always
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Square
0%
parallelogram
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Rectangle
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Rhombus
Explanation
It is obvious
A(a,and B(-a,are two fixed points of triangle ABC. The vertex C moves in such a way that cot A + cot B = λ , where λ is a constant.Then the locus of the point C is
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yλ = 2a
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ya = 2λ
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y = λa
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None of these
A pole stands vertically inside a triangular park ABC. If the angle of elevation of the top of the pole from each corner of the park is the same, then in the ∆ABC, the foot of the pole is at the
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0%
Centroid
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Circumcentre
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Incentre
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Orthocentre
The point A divides the join of the points (-5,and (3,in the ratio k : 1and the co-ordinates of the points B and C are (1,and (7,-respectively. If the area of the triangle ABC be 2 units , then k =
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6,7
0%
2)
0%
0%
7,9
The area of a triangle is 5. If two of its vertices are (2,1), (3,-and the third vertex lies on the line y = x + 3, then the third vertex is
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0%
2)
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0%
P(3,, Q(6,and R (x,y) are three points such that the angle PRQ is a right angle and the area of the ∆RPQ = 5, then the number of such points R is
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0%
0
0%
1
0%
2
0%
4
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0%
2)
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0%
The points P is equidistant from A(1,, B(-3,and C(5,-1). Then PA =
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5
0%
2)
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25
0%
The point which divides externally the line joining the points (a + b, a – b) and (a – b ,a + b) in the ratio a : b, is
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0%
0%
2)
0%
0%
None of these
The co-ordinates of the points A,B,C are (
x
1
,
y
1
), (
x
2
,
y
2
), (
x
3
,
y
3
) and D divides the line AB in the ratio
l
: k . If P divides the line DC in the ratio m : k +
l
, then the co-ordinates of P are
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0%
0%
2)
0%
0%
None of these
If A(3,5), B(–5,–, C(7,are the vertices of a parallelogram, taken in the order , then the co-ordinates of the fourth vertex are
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(10,19)
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(15,10)
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(19,10)
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(19,15)
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(15,19)
The vertices A,B,C of a triangle are (2,1), (5,and (3,respectively. Then the circumcentre is
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0%
2)
0%
0%
0%
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0%
0%
2)
0%
0%
None of the above
Explanation
It is obvious
The distance between the orthocentre and circumcentre of the triangle with vertices
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0%
2)
0%
0%
0
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0%
2)
0%
0%
None of these
The locus of the mid-point of the distance between the axis of the variable line x cos α + y sin α = p , where p is constant,
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0%
2)
0%
0%
A point moves such that the sum of its distances from two fixed points (ae,and (–ae,is always 2a. Then equation of its locus is
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0%
2)
0%
0%
None of these
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A circle
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A parabola
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An ellipse
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None of these
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0%
2)
0%
0%
The locus of a point whose difference of distance from points (3,and (–3,is 4, is
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0%
0%
2)
0%
0%
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0%
2)
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A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circum circle of the triangle PQR at the point T. If S is not the centre of the circumcircle , then
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0%
2)
0%
0%
0%
Both (and (4)
Normals are drawn at points P,Q and R lying on the parabola y
2
= \'4x which intersect at (3,0). Then match the conditions/expression in column-I with statement in column II
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A→p; B→q; C→s; D→r
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A→q; B→p; C→r; D→s
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A→r; B→q; C→p; D→s
0%
A→s; B→r; C→q; D→p
Area of the triangle with vertices (a,b), (x
1
, y
1
) and (x
2
, y
2
), where a, x
1
and x
2
are in G.P with common ratio r and b, y
1
and y
2
are in G.P. with common ratio s, is given by
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0%
2)
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0%
The co-ordinates axes are rotated through an angle 135
o
.If the co-ordinates of a point P in the new system are known to be (4,-, then the coordinates of P in the original system are
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0%
0%
2)
0%
0%
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