List of top Mathematics Questions on Straight lines

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 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 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 \(P(\alpha,\alpha+1)\) 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

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 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

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 \[ OH= \]

If the straight lines $x + 2y - 9 = 0$, $3x + 5y - 5 = 0$ and $ax + by - 1 = 0$ are concurrent, then the straight line $22x - 35y = 1$ passes through the point:

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 distance between the parallel lines $5x + 12y - 3 = 0$ and $5x + 12y + 10 = 0$ is:

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

A straight line makes equal negative intercepts on the coordinate axes. If the perpendicular distance from the origin to the line is 4 units, then the equation of the line is ......

If the angle made by the lines represented by the equation \(ax^2+2hxy+by^2 = 0\) with X-axis are \(α\) and \(β\), then \(tan(α+β)\) is

If the equation \(16x^2-24xy+9y^2-8x+6y-35 = 0\) represents a pair of straight lines, then the equation of the locus of points equidistant from these two lines is..........

The area of a triangle formed by a line with the coordinate axes is \(49\) sq. units. If the perpendicular drawn from the origin to this line makes an angle of \(45^{\circ}\) with the positive X-axis, then the equation of line is....

If two lines represented by \(x^2-(1+\sqrt{3})xy+\sqrt{3}y^2 = 0\) make angles \(α\) and \(β\) with the X-axis, then \(tan(α+β)\) is...

The family of straight lines \(4ax+3by+c = 0\) such that \(a+b+c = 0\) (where a, b, c are real constants) are concurrent at the point...

If the combined equation of angle bisectors of the lines \(x^2-2pxy-y^2 = 0\) is \(x^2-2qxy-y^2 = 0\), then which of the following is true?

A straight line L passes through the point of intersection of the lines \(x-y+1 = 0\) and \(2x+y-7 = 0\). If L intersects the positive x-axis at \(A(a,0)\) and the positive y-axis at \(B(0,b)\), then the minimum area of the triangle \(OAB\) (where \(O\) is the origin) is ....

The combined equation of lines parallel to the coordinate axes and passing through the point of intersection of lines represented by \(x^2-6xy+5y^2+10x-14y+9 = 0\) is \(\ldots\)

The coordinates of the orthocenter of the triangle whose sides are represented by the lines \(4x-7y+10 = 0\), \(x+y = 5\) and \(7x+4y = 15\) are \(\ldots\)

The line \(L_1\) given by \(\frac{x}{p}+\frac{y}{2} = 1\) passes through the point \((5,0)\). The line \(L_2\) given by \(\frac{x}{10}+\frac{y}{q} = 1\) is parallel to \(L_1\). Then the distance between the lines \(L_1\) and \(L_2\) is...

Two lines are given by \(x^2-4xy+4y^2+kx-2ky = 0\), then the value of k so that the distance between them is 3 is

The negation of \((p∧q)\rightarrow ((p∨r)\rightarrow \,\sim q)\) is equivalent to ...