List of top Mathematics Questions on Straight lines asked in AP EAPCET

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:

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

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:

Number of triangles formed by the lines \[ x-y+3=0,\quad 2x-y+3=0,\quad 3x-y+2=0 \] and \[ x+y-3=0 \] is

The distance between the lines represented by \[ 4x^2+20xy+25y^2+2x+5y-12=0 \] is equal to

For the three points \(A(2,0)\), \(B(0,2)\) and \(P(1,1)\), suppose \(d\) is the algebraic sum of the distances of \(A\) and \(B\) from a line that passes through \(P\). Then which of the following is correct?

If a point \((\alpha,\beta)\) of \(3x+y=0\) and \((3,4)\) lie on the opposite sides of \(3x-4y-8=0\), then which of the following is correct?

If a particle moving along \[ x-2y-3=0 \] gets reflected in a perpendicular direction upon hitting the line \[ 3x-2y-5=0, \] then the line of movement of the particle after reflection is

If two distinct points lying at a unit distance from \[ 4x+3y-10=0 \] and passing through \[ x+y=4 \] are separated by a distance \(d\), then the value of \(d\) is

Suppose \(P(x,y)\) lying on \[ \sqrt{3}x-y+2=0 \] or \[ \sqrt{3}x+y-2=0 \] is at a distance of \(5\) units from their point of intersection. Then the distance from \((0,0)\) to the foot of the perpendicular of \(P\) onto the \(y\)-axis is

Suppose the pairs of straight lines \[ 2x^2+axy+3y^2=0 \] and \[ 2x^2+bxy-3y^2=0 \] are such that they have one common line with the other two remaining perpendicular. Then the values of \(a\) and \(b\) respectively are:

The locus of the incentre of the triangle formed by the lines \[ xy-4x-4y+16=0 \] and \[ x+y=5 \] is

Suppose a point \(P\) moves so that \[ BP^2-AP^2=121, \] where \(A\) and \(B\) are \((2,5)\) and \((5,11)\) respectively. Then the locus of \(P\) is a straight line, whose slope is:

Suppose that the sides passing through the vertex \((\alpha,\beta)\) of a triangle are bisected at right angles by the lines \[ y^2-8xy-9x^2=0. \] Then the centroid of the triangle is

Suppose the slopes \(m_1\) and \(m_2\) of the lines represented by \[ ax^2+2hxy+by^2=0 \] satisfy \[ 3(m_1-m_2)-7=0 \] and \[ m_1m_2-2=0. \] Then which of the following is true?

Suppose \(P\) and \(Q\) lie on \[ 3x+4y-4=0 \] and \[ 5x-y-4=0 \] respectively. If the midpoint of \(PQ\) is \((1,5)\), then the slope of the line passing through \(P\) and \(Q\) is

The length of intercept of \[ x+1=0 \] between the lines \[ 3x+2y=5 \] and \[ 3x+2y=3 \] is

Suppose that the three points \(A\), \(B\) and \(C\) in the plane are such that their \(x\)-coordinates as well as \(y\)-coordinates are in G.P. with the same common ratio. Then the points \(A\), \(B\) and \(C\)

If the points of intersection of the coordinate axes and \(|x+y|=2\) form a rhombus, then its area is

Suppose, in triangle \(\triangle ABC\), \(x-y+5=0\), \(x+2y=0\) are respectively the equations of the perpendicular bisectors of the sides \(AB\) and \(AC\). If \(A=(1,-2)\), the equation of the line joining \(B\) and \(C\) is

If the pair of straight lines \[ 9x^2+axy+4y^2+6x+by-3=0 \] represents two parallel lines, then

A line passing through \(P(2,3)\) and making an angle of \(30^\circ\) with the positive direction of \(x\)-axis meets \[ x^2-2xy-y^2=0 \] at \(A\) and \(B\). Then the value of \(PA\cdot PB\) is

For \(a,b,h>0\), if the slope of one of the lines represented by \[ a^2x^2+2hxy+b^2y^2=0 \] is twice that of the other, then the value of \[ \frac{h}{ab} \] is:

Suppose \(A\) and \(B\) are the points at which the line \[ x+y-\lambda=0 \] meets the pair of straight lines \[ x^2+y^2-2x-4y+2=0. \] If \(\angle AOB=90^\circ\), then the value of \(\lambda\) is: