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 ?