List of top Mathematics Questions on Straight lines asked in MET

The equation to the line through the point of intersection of \(x - y + 1 = 0\), \(3x + 2y + 4 = 0\) and perpendicular to \(x - 4y = 0\) is

The ratio in which the segment joining \((2,1)\) and \((0,-2)\) is divided by the line \(2x - 3y + 4 = 0\) is

A line cuts off on the coordinate axes positive intercepts whose sum is 4. If it passes through \((9/2,-5)\), its equation is

If \(A(-1,2)\), \(B(5,1)\), \(C(6,5)\) are the vertices of a parallelogram \(ABCD\). The equation to the diagonal through \(B\) is

The point on the line \(y = x\) equidistant from \((4,0)\) and \((5,1)\) is

If point \(D\) divides base \(BC\) of \(\triangle ABC\) in ratio \(m:n\), then value of \(mBD^2 + nCD^2 + (m+n)AD^2\) is:

The three lines of a triangle are given by \((x^2 - y^2)(2x + 3y - 6) = 0\). If the point \((-2,\lambda)\) lies inside and \((\mu,1)\) lies outside the triangle, then

The equation of bisectors of the angles between the lines \(|x| = |y|\) are

The base of vertices of an isosceles triangle PQR are Q(1, 3) and R(-2, 7). The vertex P can be

If the angles between the pair of straight lines represented by the equation \(x^2 - 3xy + \lambda y^2 + 3x - 5y + 2 = 0\) is \(\tan^{-1}(1/3)\). Where \(\lambda\) is a non-negative real number, then \(\lambda\) is

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

$A(-1,2)$, $B(5,1)$, $C(6,5)$ are the vertices of a parallelogram $ABCD$. The equation of the diagonal through $B$ is

The product of the perpendiculars from $(-1, 2)$ to the pair of lines $2x^{2} - 5xy + 2y^{2} + 3x - 3y + 1 = 0$ is

The line $\frac{x}{a} - \frac{y}{b} = 1$ cuts the x-axis at P. The equation of the line through P perpendicular to the given line is

If the angle between two lines represented by $2x^2 + 5xy + 3y^2 + 7y + 4 = 0$ is $\tan^{-1} m$, then m is equal to

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

The intercepts on the straight line \(y = mx\) by the lines \(y = 2\) and \(y = 6\) is less than 5, then \(m\) belongs to

The equations of the lines passing through the point \( (1,0) \) and at a distance \( \frac{\sqrt{3}}{2} \) from the origin are

The distance of the point (3, 5) from $2x + 3y -14 = 0$ measured parallel to $x - 2y = 1$ is

If the line \( \frac{x}{a} + \frac{y}{b} = 1 \) moves such that \( \frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{c^2} \), then the locus of the foot of the perpendicular from the origin to the line is

If \(\int \frac{dx}{x^2(x^n + 1)^{(n-1)/n}} = -[f(x)]^{1/n} + c\) then \(f(x)\) is

\(\int \sqrt{1 + \csc x} dx\) is equal to

Which one of the following is independent of \(\alpha\) in the hyperbola \((0<\alpha<\pi/2)\) \(\frac{x^2}{\cos^2 \alpha} - \frac{y^2}{\sin^2 \alpha} = 1\)?

The tangents to \(x^2 + y^2 = a^2\) having inclinations \(\alpha\) and \(\beta\) intersect at \(P\). If \(\cot \alpha + \cot \beta = 0\), then the locus of \(P\) is

Minimum distance between the curves \(y^2 = 4x\) and \(x^2 + y^2 - 12x + 31 = 0\) is