List of top Mathematics Questions on Horizontal and vertical lines

Let \(\alpha, \beta, \gamma\) be the foot of perpendicular from the point \((1, 2, 3)\) on the line \(\frac{x + 3}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}\). Then \(19(\alpha + \beta + \gamma)\) is equal to:

Let \((\alpha, \beta, y)\) be the foot of perpendicular form the point \((1,2,3)\) on the line \(\bigg(\frac{x + 3}{5}\) = \(\frac{y - 1}{2}\) = \(\frac{z + 4}{3}\) \(\bigg)\)then \(19 (\alpha + \beta + y)\)

Let A(α, -2), B(α, 6) and C(\(\frac{\alpha}{4}\), -2) be vertices of a ΔABC. If (5, \(\frac{\alpha}{4}\)) is the circumcentre of ΔABC, then which of the following is NOT correct about ΔABC?

If $4a^2 + b^2 + 2c^2 + 4ab - 6ac - 3bc = 0$, the family of lines $ax + by + c = 0$ is concurrent at one or the other of the two points-

The distance between the parallel lines $ y=x+a,\,\,y=x+b $ is

A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2 + y^2 = 4$ with $x + y = a$. The set containing the value of '$a$' is

The area enclosed by the pair of lines $xy = 0$ , the line $x - 4 = 0$ and $y + 5 = 0$ is

The distance between the pair of parallel lines $ x^2 + 2xy + y^2 - 8ax - 8ay - 9a^2 = 0$ is :

If the two pair of lines $ {{x}^{2}}-2mxy-{{y}^{2}}=0 $ and $ {{x}^{2}}-2nxy-{{y}^{2}}=0 $ are such that one of them represents the bisector of the angles between the other, then:

The lines x + 2y - 5 = 0, 2x - 3y + 4 = 0, 6x + 4y - 13 = 0

The distance between the parallel lines $9x^2 - 6xy + y^2 +18x - 6y + 8 = 0$ is

The area of the parallelogram formed by the lines $ax+by+c_1=0, \: ax+by+c_2=0, \: px+qy+r_1=0, \: px+qy+r_2=0$