Coordinate System and Straight Line · Mathematics · NDA

The number of points represented by the equation $x = 5$ on the $xy$-plane is

If a variable line passes through the point of intersection of the lines $x + 2y - 1 = 0$ and $2x - y - 1 = 0$ and meets the coordinate axes in $A$ an...

What is the equation to the straight line passing through the point $(-sin\theta, cos\theta)$ and perpendicular to the line $xcos\theta + ysin\theta =...

Two points $P$ and $Q$ lie on line $y = 2x + 3$. These two points $P$ and $Q$ are at a distance 2 units from another point $R(1, 5)$. What are the coo...

If two sides of a square lie on the lines $2x + y - 3 = 0$ and $4x + 2y + 5 = 0$, then what is the area of the square in square units?

ABC is a triangle with A(3, 5). The mid-points of sides AB, AC are at (-1, 2), (6, 4) respectively. What are the coordinates of centroid of the triang...

ABC is an acute angled isosceles triangle. Two equal sides AB and AC lie on the lines 7x - y - 3 = 0 and x + y - 5 = 0. If θ is one of the equal angle...

Let $x+2 y+1=0$ and $2 x+3 y+4=0$ are two lines of regression computed from some bivariate data. If $\theta$ is the acute angle between them, then wha...

The points (-a, -b), (0, 0), (a, b) and (a2, ab) are:...

Given that 16p2 + 49q2 - 4r2 - 56pq = 0. Which one of the following is a point on a pair of straight lines (px + qy + r) (px ...

For what values of k is the line (k - 3)x - (5 - k2) y + k2 - 7k + 6 = 0 parallel to the line x + y = 1?...

The line x + y = 4 cuts the line joining P(-1, 1) and Q(5, 7) at R. What is PR ∶ RQ equal to ?

What is the sum of the intercepts of the line whose perpendicular distance from origin is 4 units and the angle which the normal makes with positive d...

What is the equation of diagonal through origin ? 

What is the equation of other diagonal ?  

If two lines of regression are x + 4y + 1 = 0 and 4x + 9y + 7 = 0, then what is the value of x when y = -3 ? 

A bivariate data set contains only two points (-1, 1) and (3, 2). What will be the line of regression of y on x ?

Consider the following statements in respect of the line passing through origin and inclining at an angle of 75° with the positive direction of x-axis...

If P(3, 4) is the mid-point of a line segment between the axes, then what is the equation of the line?

The base AB of an equilateral triangle ABC with side 8 cm lies along the y-axis such that the mid-point of AB is at the origin and B lies above the or...

Consider the inequations 5x - 4y + 12 < 0, x + y < 2, x < 0 and y > 0. Which one of the following points lies in the common region?

If the points with coordinates (-5, 0), (5p2, 10p) and (5q2, 10q) are collinear, then what is the value of pq where p ≠ q ?

What is the equation of the straight line which passes through the point (1, -2) and cuts off equal intercepts from the axes ?

A straight line passes through the point of intersection of x + 2y + 2 = 0 and 2x - 3y - 3 = 0. It cuts equal intercepts in the fourth quadrant. What ...

Under which one of the following conditions are the lines ax + by + c = 0 and bx + ay + c = 0 parallel (a ≠ 0, b ≠ 0)?

What is the equation of the locus of the mid-point of the line segment obtained by cutting the line x + y = p, (where p is a real number) by the coord...

If the point (x, y) is equidistant from the points (2a, 0) and (0, 3a) where a > 0, then which one of the following is correct ?