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List of top Mathematics Questions on Straight lines asked in KEAM

If the two sides AB and AC of a triangle are along \(4x-3y-17 = 0\) and  \(3x+4y-19= 0\), then the equation of the bisector of the angle between AB and AC is ?
Suppose the point \(P(1,1)\) is translated to \(Q\) in the direction of y = 2x. If \(PQ = 1\),then Qis
Suppose the line mx-y+ 5m-4=0 meets the lines x+3y+2=0, 2x+3y+4=0 and x-y-5=0 at the points R. S and T, respectively. If R, S and T are at distances r1, r2 and r3, respectively, from (-5,-4) and \((\frac{15}{r_1})^2+(\frac{10}{r_2})^2=(\frac{6}{r_3})^2\) then the value of m is

A point moves in such a way that it remains equidistant from each of the lines \(3x±2y= 5\). Then the path along which the point moves is?

Suppose a line parallel to \(ax+by=0\) (where \(b≠0\))intersects\( 5x-y+4=0\) and \(3x+4y-4=0\) ,respectively at P and Q. If the midpoint of PQ is \((1,5)\),then the value of \(\dfrac{a}{b}\) is

If the \(XZ\)-plane divides the straight line joining the points \((2,4,7)\) and \((3,-5,8)\)  in the ratio \(α:1\),then the value of \(α\) is ? 

If a straight line in XY plane is passes through \((-a,-b),(a,b),(k,k),(a^2,a^3)\) for some real number \(a,b\) and \(k\),where \(a≠0\),then which of the following option is correct?

The line perpendicular to \(4x-5y+1=0\) and passing through the point of intersection of the straight line \(x+2y-10=0\) and \(2x+y+5=0\) is ?
If the line y = mx + c is perpendicular to y=1+x and passes through the point (1, 2), then the value of c is equal to
The equation of the straight line parallel to y=-3x and passing through the point (3,-2) is
The equation of the line which is parallel to \(x+\frac{1}{2}y=\frac{3}{2}\) and passing through (1,3) is
If x-intercept of the straight line ax+2ay=30 is 10, then the y-intercept is
A straight line makes an angle a with the positive direction of x-axis, where \(\cos a=\frac{\sqrt3}{2}\). If it passes through (0,-2), then its equation is
The y-intercept of the line passing through (2, 5) with slope \(\frac{1}{2}\) is equal to
Triangle $ABC$ has vertices $(0, 0), (11, 60)$ and $(91, 0)$. If the line $ y=kx $ cuts the triangle into $2$ two triangles of equal area, then $k$ is equal to
The $ x- $ axis, $ y- $ axis and a line passing through the point A (6, 0) form a triangle $ABC$. If $ \angle A=30{}^\circ , $ then the area of the triangle, in sunits is
If a straight line passes through the points $ \left( \frac{-1}{2},1 \right) $ and $(1, 2)$, then its $x$-intercept is
Let $O$ be the origin and $A$ be the point $(64, 0).$ If $P$, $Q$ divide $OA$ in the ratio $1 : 2 : 3$ , then the point $P$ is
Let $A (6, -1), B (1, 3)$ and $C (x, 8)$ be three points such that $AB = BC$. The values of $x$ are
The locus of a point which is equidistant from the points $(1,1)$ and $(3, 3)$ is
If the distance between the two points $(-1, a )$ and $(-1, -4a )$ is $10$ units, then the values of $a$ are
The area of the triangle formed by the points $(2, 2), (5, 5), (6, 7)$ is equal to (in square units)
Area of the triangle with vertices $(- 2, 2), (1, 5) $and $(6, - 1)$ is

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