The cartesian plane - class-XI
Description: the cartesian plane | |
Number of Questions: 33 | |
Created by: Prajapati Rathore | |
Tags: coordinate geometry graphs lines graph prerequisites coordinates co-ordinate geometry maths linear graphs position and movement |
A Cartesian plane consists of two mutually _____ lines intersecting at their zeros.
The coordinates of the point of intersection of X-axis and Y-axis is( 0,0)
State true or false.
The coordinates of a point on __axis are (0, y).
The horizontal axis is called ______ axis.
A pair of numerical coordinates is required to specify each point in a ......... plane.
Which statement is true?
Equation of the line $y = 0$ represents :
Slope of the line $AB$ is $-\dfrac {4}{3}$. Co-ordinates of points $A$ and $B$ are $(x, -5)$ and $(-5, 3)$ respectively. What is the value of $x$
The coordinates of $A, B$ and $C$ are $(5, 5), (2, 1)$ and $(0, k)$ respectively. The value of $k$ that makes $\overline {AB} + \overline {BC}$ as small as possible is
If the coordinates of vertices of a triangle is always rational then the triangle cannot be
The abscissa of two points A and B are the roots of the equation ${x^2} + 2ax - {b^2}$ and their ordinates are the root of the equation ${x^2} + 2px - {q^2}=0$. the equation of the circle with AB as diameter is
The acute angle between the lines $x-y=0$ and $y=0$ is
If the distance between the points $\left( {a\,\cos {{48}^ \circ },0} \right)$ and $\left( {\,0,a\,\cos {{12}^ \circ }} \right)$ is d,then ${d^2} - {a^2} = $
If the points $A ( 2,1,1 ) , B ( 0 , - 1,4 ) , C ( K , 3 , - 2 )$ are collinear then $K =$
Find the number of points on the straight line which joins $\left( { - 4,\,11} \right)$ to $\left( { 16,\,- 1} \right)$ whose co-ordinates are positive integer.
If the points $( 2,0 ) , ( 0,1 ) , ( 4,5 ) \text { and } ( 0 , c )$ are concyclic then the value of $c$ is
If points $( - 7,5 ) \text { and } \left( \alpha , \alpha ^ { 2 } \right)$ lie on the opposite sides of the line $5 x - 6 y - 1 = 0$ then
If the three distinct points $\left( t,2at+{ at }^{ 3 } \right)$ for $i=1,2,3$are collinear then the sum of the abscissa of the _________.
The abscissa of a point on the curve $xy=(a+x)^{2}$, the normal cuts off numerically equal intercepts from the coordinate axes, is
To remove Xy term from the second degree equation $5x^2 + 8xy + 5y^2 + 3x + 2y + 5 = 0$, the coordinates axes are rotated through an angle q, then q equals.
A line located in a space makes equal angle with the co-ordinate axis then angle makes by line from anyone axis are-
$C$ is a point on the line segment joining the points $A(2,-3,4)$ and $B(8,0,10)$. If the value of $y$-coordinate of $C$ is $-2$, then the $z-$coordinate of $C$ is
The area of the triangle formed y a tangents to the curve $2xy=a^{2}$ and the coordinates axes is
If a point P from where line drawn cuts coordinate axes at A and B(with A on x-axis and B on y-axis) satisfies $\alpha\cdot \dfrac{x^2}{PB^2}+\beta\dfrac{y^2}{PA^2}=1$, then $\alpha +\beta$ is?
If the points $(k, 2 - 2k), (1 - k, 2k)$ and $(-k -4, 6 - 2k)$ be collinear the possible value(s) of $k$ is/are
The points (1, -1), $\displaystyle \left ( -\frac{1}{2},\frac{1}{2} \right )$ and (1, 2) are the vertices of an isosceles triangle
The point $(5,\,3)$ lies on line $3x+2y=18$
Identify the true statement.
If a point $P$ has coordinates $(3,4)$ in a coordinate system $X'OX\leftrightarrow Y'OY$, and if $O$ has coordinates $(4,3)$ in another system ${X} {1}'{O} _{1}{X} _{1}\leftrightarrow {Y} _{1}'{O} _{1}{Y} _{1}$ with $X'OX\parallel {X} _{1}'{O} _{1}{X} _{1}$, then the coordinates of $P$ in the new system ${X} _{1}'{O} _{1}{X} _{1}\leftrightarrow {Y} _{1}'{O} _{1}{Y} _{1}$ is _______________
Let a, b, c and d be non-zero numbers. If the point of intersection of the lines $4ax+2ay+c=0$ and $5bx+2by+d=0$ lies in the fourth quadrant and is equidistant from the two axes then
The points $A\left( {2a,\,4a} \right),\,B\left( {2a,\,6a} \right)\,$ and $C\left( {2a + \sqrt 3 a,\,5a} \right)$ (when $a>0$) are vertices of
Mid point of $A(0, 0)$ and $B(1024, 2050)$ is ${A _1}$. mid point of ${A _1}$ and B is ${A _2}$ and so on. Coordinates of ${A _{10}}$ are.
If the coordinates of the extermities of diagonal of a square are $(2,-1)$ and $(6,2)$, then the coordinates of extremities of other diagonal are