List of top Mathematics Questions on Straight lines

If two lines drawn from a point $P(2,3)$ intersect the line $x+y=6$ at a distance $\sqrt{\dfrac{2}{3}}$, then the angle between the lines is

Let chord $PQ$ of length $3\sqrt{13}$ of the parabola $y^2 = 12x$ be such that the ordinates of points $P$ and $Q$ are in the ratio $1:2$. If the chord $PQ$ subtends an angle $\alpha$ at the focus of the parabola, then $\sin \alpha$ is equal to:

Consider the lines \[ L_1: 2x+3y+1=0 \] and \[ L_2: 3x-2y+1=0. \] The locus of a variable point that is equidistant from the two lines \(L_1=0\) and \(L_2=0\) is

If the slope of one of the lines is twice the slope of the other in the pair of straight lines \[ 6x^2+2hxy+y^2=0, \] then \[ |h|= \]

If the equation \[ \lambda x^2-5xy+6y^2+x-3y=0 \] represents a pair of straight lines, then the point of intersection of these straight lines is

The lines \[ L_1:2x+y+1=0 \] and \[ L_2:x-2y+4=0 \] intersect at \(A\). Let \(P\) be a point at a distance \(5\) units from \(L_1=0\) and \(\alpha\) units from \(L_2=0\). If \(M\) and \(N\) are the feet of the perpendiculars from \(P\) on the lines \(L_1=0\) and \(L_2=0\) respectively, and the area of the quadrilateral \(AMPN\) is \(25\) sq. units, then the point \(P\) lies on the line

If \(P(\alpha,\alpha+1)\) is the foot of the perpendicular drawn from the origin to the line \(L\) and the \(x\)-intercept of \(L\) is \[ \left(-\frac52,0\right), \] then the sum of the squares of the distances from the origin to all such possible points \(P\) is

Area of Triangle with point (1,2) (3,6) (5,10) is

The point dividing (1, 2) and (5, 6) in ratio 1:3 internally

If the equation of a line passing through \[ \left(\frac13,-\frac12\right) \] and making an angle of \(60^\circ\) with the line \[ 2x-3y+4=0 \] is \[ (2+3\sqrt3)x+by=c, \] then \(c=\)

If the angular bisectors of the lines \[ 3x-4y-5=0 \] and \[ 8x-6y+1=0 \] are \[ x+y+c=0 \] and \[ x-y+k=0, \] then \[ 7(c+k)= \]

If \(O\) is the origin and \(H\) is the orthocenter of a triangle formed by the lines \[ x+y=1, \] \[ 6x^2-13xy+6y^2=0, \] then \[ OH= \]

The straight line passing through the points $(1, 5)$ and $(3, -5)$ meets the coordinate axes at the points $A$ and $B$. Then the area of the triangle $\triangle OAB$, where $O$ is the origin, is

If the equation of the straight line passing through the points $(3, -4)$ and $(4, a)$ is $x - y = 7$, then the value of $a$ is equal to

A point C lies on the perpendicular bisector of the straight-line segment joining the points A(-3,-6) and B(13,-6). If the point C lies in the first quadrant and the distance between the point C and the midpoint of AB is 8 units, then the coordinates of C are

Let A(-4,3), B(0,5) and C(-1,2) be three points. The equation of the straight line which passes through C and bisects the straight-line segment AB is

If the image of the point (2,6) in the line \(x-3y+10=0\) is (h,k), then \(2h-k=\)

Assuming that the straight line works as a plane mirror for a point, the image of the point \((1,2)\) in the line \[ x-3y+4=0 \] is

The orthocentre of the triangle formed by the following straight lines is \[ y=x,\qquad x-2y+1=0,\qquad 3x-4y-1=0 \]

If the inclination of a straight line \[ x-y+1=0 \] with another straight line \(L\) is \(30^\circ\) and \(m\) is the slope of line \(L\), then \[ m^2+1= \]

If \(A(2,1)\), \(B(4,k)\), \(C(3,4)\) are vertices of triangle right angled at B and \(k\) is not an odd number, then equation of line joining orthocentre and circumcentre is

The equation of the lines through \( (1, 1) \) and making angles of \( 45^\circ \) with the line \( x + y = 0 \) are:

Let the line \(L_1 : x + 3 = 0\) intersect the lines \(L_2 : x - y = 0\) and \(L_3 : 3x + y = 0\) at the points A and B, respectively. Let the bisector of the obtuse angle between the lines \(L_2\) and \(L_3\) intersect the line \(L_1\) at the point C. Then \(BC^2 : AC^2\) is equal to:

The distance of the point $(1, 2)$ from the line $3x + 4y - 32 = 0$ measured parallel to the line $x - y = 0$ is:

The foot of the perpendicular from the point $(1, 3)$ to the line $x + y - 2 = 0$ is: