Mathematics · Quantitative Aptitude

Coordinate Geometry

221 Questions

Practice fundamental coordinate geometry questions covering reflections, collinear points, and loci. This collection helps in mastering XY plane plots, midpoints, and quadrant identification. It is highly beneficial for students preparing for quantitative aptitude tests, JEE, and state level engineering exams.

Point reflectionCollinear pointsXY plane lociFinding midpointsCoordinate quadrantsRhombus vertices

Coordinate Geometry Questions

Multiple choice maths unchanging relations algebra aid introduction to unknowns measures and relations

If the point (2, -3) lies on $\displaystyle kx^{2}-3y^{2}+2x+y-2=0$ then k is equal to 

  1. $\displaystyle \frac{1}{7}$

  2. 16

  3. 7

  4. 12
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

As the point lies on the given line, it should satisfy the equation of the line, if we substitute $ x = 2 $ and $ y = -3 $ in it.

So, $k({ 2) }^{ 2 }3{ (-3) }^{ 2 }+2(2)-32=0$
$ => 4k -27 + 4 - 3 -2 = 0 $
$ 4k = 28 $
$ k = 7 $

Multiple choice position of point wrt ellipse ellipse maths

The locus of a point whose distance form the point $(3,0)$ is $3/5$ times its distance from the line $x=p$ is an ellipse with centre at the origin. The value of $p$ is 

  1. $5$
  2. $7$
  3. $\dfrac{25}{3}$
  4. $\dfrac{25}{9}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The definition of an ellipse is the locus of a point whose distance from a focus is e times its distance from the directrix. Here e = 3/5 and the focus is (3,0). The directrix is x=p, so the equation is sqrt((x-3)^2 + y^2) = (3/5)|x-p|. Squaring both sides and simplifying to the form x^2/a^2 + y^2/b^2 = 1, we find the center is at (ae, 0). Since the center is at the origin, the focus must be at (ae, 0), implying ae = 3. With e = 3/5, a = 5. The directrix is x = a/e = 5/(3/5) = 25/3.

Multiple choice position of point wrt ellipse ellipse maths

Position of a point $(3,-4))$ with respect to the ellipse $16x^{2}+9y^{2}=144$ lies 

  1. outside

  2. inside

  3. on

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given equation is $16{ x }^{ 2 }+9{ y }^{ 2 }=144$

$ f(x,y)=16{ x }^{ 2 }+9{ y }^{ 2 }-144\ f(3,-4)=16{ (3) }^{ 2 }+9(-4)^{ 2 }-144\ f(3,-4)=144+144-144\ f(3,-4)=144\ f(3,-4)>0$
So, the point lies outside the ellipse.

Option A is correct.

Multiple choice position of point wrt ellipse ellipse maths

Let $(a, 0)$ and $B(b, 0)$ be fixed distinct points on the $x-axis$, none of which coincides with the origin $O(0, 0)$ and let $C$ be a point on the $y-axis$. Let $L$ be a line through the $O(0, 0)$ and perpendicular to the line $AC$, The locus of the point of intersection of lines $L$ and $BC$ if $C$ varies along the $y-axis$, is (provided $x^{2}+ab\neq 0$) 

  1. $\dfrac{x^{2}}{a}+\dfrac{y^{2}}{b}=x$
  2. $\dfrac{x^{2}}{a}+\dfrac{y^{2}}{b}=y$
  3. $\dfrac{x^{2}}{b}+\dfrac{y^{2}}{a}=x$
  4. $\dfrac{x^{2}}{b}+\dfrac{y^{2}}{a}=y$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let C = (0, c). A = (a, 0), B = (b, 0). Line AC: y - 0 = (c-0)/(0-a) * (x-a) => y = -c/a * (x-a). Line L is perpendicular to AC through origin: y = a/c * x. Line BC: y - 0 = (c-0)/(0-b) * (x-b) => y = -c/b * (x-b). Solving for the intersection of L and BC by eliminating c, we get x^2/b + y^2/a = y.

Multiple choice position of point wrt ellipse ellipse maths

The point $(4, -3)$ with respect to the ellipse $4x^2+5y^2=1$.

  1. lies on the curve

  2. lies inside the curve

  3. lies outside the curve

  4. lies focus of the curve
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$Equation\quad of\quad ellipse:\quad 4{ x }^{ 2 }+5{ y }^{ 2 }=1\ Putting\quad the\quad point\quad (4,-3)\quad on\quad the\quad ellipse\quad we\quad get:\ \quad =4{ (4) }^{ 2 }+5{ (-3) }^{ 2 }-1\ =\quad 64+45-1=28>0\ \therefore \quad The\quad point\quad lies\quad outside\quad the\quad ellipse.$


Option [C]

Multiple choice maths arithmetic progressions complete the a.p series with given information properties of an ap problems on ap

If $a,b,c$ are in $A.P.$, then the straight lines $ax+by+c=0$ wil always pass through the point ..........

  1. $(1,2)$
  2. $(1,5)$
  3. $(3,2)$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$A,B, C$ in $AP$


$ax + by + c = 0$ __(I)


$\therefore 2b = a + c$

$a - 2b + c = 0$ __(II)

comparing (I) and (II),

$x = 1, y = -2$

$\therefore (1, -2)$ is the fixed point

Multiple choice

The set of all points in the plane that are in the first quadrant is called a:

  1. Quadrant.

  2. Octant.

  3. Hemisphere.

  4. Sextant.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The set of all points in the plane that are in the first quadrant is called a quadrant.

Multiple choice

What is the number of ways to triangulate a convex (n)-gon with (k) interior points?

  1. \(S_{n+k}\)
  2. \(C_{n+k}\)
  3. \(S_{n+k} + C_{n+k}\)
  4. \(S_{n+k} - C_{n+k}\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The number of ways to triangulate a convex (n)-gon with (k) interior points is given by the Schröder number (S_{n+k}).

Multiple choice

In a Cartesian coordinate system, the point (3, -4) is located in which quadrant?

  1. I

  2. II

  3. III

  4. IV
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In the Cartesian coordinate system, the first quadrant is located in the upper right, the second quadrant is located in the upper left, the third quadrant is located in the lower left, and the fourth quadrant is located in the lower right. Therefore, the point (3, -4) is located in the fourth quadrant.