Coordinate System in 2D

A line segment $AB$ is denoted as:

The graph of $7x+3y=4$ and $5x-3y=2$, in the $y$-axis at two points having distance -

The equations are:
$$\begin{gathered} 3x+4y=10 \\ -x+2y=0 \end{gathered}$$
have the solution $(a, b)$. The value of $a+b$ is _____

Consider the location of a warehouse to distribute book for the cities of Bombay, Bangalore and Calcutta are$55,000 , 20,000$and $25,000$ units respectively. Using some appropriate origin the (x, y) co-ordinates of Bombay, Bangalore and Calcutta can be approximated as $(10, 20), (20, 10)$ and $(30,30)$ respectively. The (x,y) co ordinates of the optimal location would be

$A$ and $B$ are two fixed points $5 cm$ a part with each other and $C$ is a point on $A,B$ such that $AC$ is $3 cm$. If the length of $AC$ is increased by $6\raisebox{1ex}{$0$}\!\left/ \!\raisebox{-1ex}{$0$}\right.$, the length of CB is decreased by :

Find the coordinates of the point which divides the line joining (5, – 2) and (9, 6) internally in the ratio 1:3.

A flat surface which extends indefinitely in all directions is called ___________ .

The length of the intercept of the graph of the equation $9x-12y=108$  between the two axis is -

The length of a line segment $AB$ is $2 \mathrm{unit}$. It is divided into two part at the point $C$ such that $A{C}^2 = AB\times CB$. What is the length of CB?

Name the point of intersection in the given figure.
   

Find the distance between the point $(12,15)$ and its image through the line $6x+8y=42$?

The following parabolic curves represent a general quadratic polynomial function $y=f\left(x\right)=a{x}^2+bx+c$

Find the values of $abc$  in each case and choose the correct option

The following parabolic curves represent a general quadratic polynomial function $y=f\left(x\right)=a{x}^2+bx+c$

Find the values of $a+b+c$ in each case and choose the correct option.

The following parabolic curves represent a general quadratic polynomial function $y=f\left(x\right)=a{x}^2+bx+c$

Find the values of $a-b+c$  in each case and choose the correct option

The following parabolic curves represent a general quadratic polynomial function $y=f\left(x\right)=a{x}^2+bx+c$

Find the values of $a+b+c$  in each case and choose the correct option.

Which of the following Intersect x-axis at two distinct points?

What is the minimum or maximum value of the polynomial $3x^2 - 4x + 3$?

$4x-3=0$ is the axis of the symmetry of the parabola $y= 2x^2 + (m + 1)x - 4.$ Find the minimum value of the function.

Find the value of $pqr.$

The parabolas $y = a{x}^2 + bx + c$ and $y = a{x}^2 - bx + c$ are given. The coefficients a, b, and c are real numbers. Which one of the following statements is NOT true about the intersection of these parabolas?
$1.$ There are two intersections.
$2.$ The intersection point is not on the axes.
$3.$ The parabolas only intersect at the origin.
$4.$ The parabolas only intersect on the y-axis.
$5.$ The parabola only intersect on the x-axis