List of top Mathematics Questions on Straight lines asked in KEAM

Equation of line through \( (a,b) \) parallel to \( \frac{x}{a} + \frac{y}{b} = 1 \)

The distance of the point \( (3, -5) \) from the line \( 3x - 4y - 26 = 0 \) is:

The equation of the line passing through \( (-3, 5) \) and perpendicular to the line through the points \( (1, 0) \) and \( (-4, 1) \) is:

If the points \( (1, 0), (0, 1) \) and \( (x, 8) \) are collinear, then the value of \( x \) is equal to:

The image of the origin with respect to the line $4x + 3y = 25$ is:

If y-intercept of the line $4x - ay = 8$ is thrice its x-intercept, then the value of $a$ is equal to:

The equation of one of the straight lines passing through the point \( (0, 1) \) and is at a distance of \( \frac{3}{5} \) units from the origin is:

The nearest point on the line $x + y - 3 = 0$ from the point $(3, -2)$ is:

If the straight line \( 5x + y = k \) forms a triangle with the coordinate axes of area \(10\) sq. units, then the values of \(k\) are

If a straight line is perpendicular to \( 2x + 8y = 10 \) and meets the x-axis at \( (5,0) \), then it meets the y-axis at

The distance between the point \( (1,2) \) and the point of intersection of the lines \( 2x + y = 2 \) and \( x + 2y = 2 \) is

If \( p_1 \) and \( p_2 \) are respectively length of perpendiculars from the origin to the straight lines \( x\sec\theta + y\cosec\theta = a \) and \( x\cos\theta - y\sin\theta = a\cos 2\theta \), then \( 4p_1^2 + p_2^2 = \)

If \( p \) and \( q \) are respectively the perpendiculars from the origin upon the straight lines whose equations are \( x\sec\theta + y\csc\theta = a \) and \( x\cos\theta - y\sin\theta = a\cos 2\theta \), then \( 4p^2 + q^2 \) is equal to:

A straight line perpendicular to the line \( 2x + y = 3 \) is passing through \( (1,1) \). Its y-intercept is:

If \( p \) is the length of the perpendicular from the origin to the line whose intercepts with the coordinate axes are \( \frac{1}{3} \) and \( \frac{1}{4} \), then the value of \( p \) is:

A straight line perpendicular to the line \( 2x + y = 3 \) is passing through \( (1,1) \). Its y-intercept is:

If \( p \) and \( q \) are respectively the perpendiculars from the origin upon the straight lines whose equations are \( x\sec\theta + y\csc\theta = a \) and \( x\cos\theta - y\sin\theta = a\cos 2\theta \), then \( 4p^2 + q^2 \) is equal to:

If \( p \) is the length of the perpendicular from the origin to the line whose intercepts with the coordinate axes are \( \frac{1}{3} \) and \( \frac{1}{4} \), then the value of \( p \) is:

If \( p \) is the length of the perpendicular from the origin to the line whose intercepts with the coordinate axes are \( \frac{1}{3} \) and \( \frac{1}{4} \), then the value of \( p \) is:

A straight line perpendicular to the line \( 2x + y = 3 \) is passing through \( (1,1) \). Its y-intercept is:

If \( p \) and \( q \) are respectively the perpendiculars from the origin upon the straight lines whose equations are \( x\sec\theta + y\csc\theta = a \) and \( x\cos\theta - y\sin\theta = a\cos 2\theta \), then \( 4p^2 + q^2 \) 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

Let $A (6, -1), B (1, 3)$ and $C (x, 8)$ be three points such that $AB = BC$. The values of $x$ are

If the distance between the two points $(-1, a )$ and $(-1, -4a )$ is $10$ units, then the values of $a$ are