List of top Mathematics Questions on Distance of a Point From a Line

If the image of the point $ P(1, 2, a) $ in the line \[ \frac{x - 6}{3} = \frac{y - 7}{2} = \frac{7 - z}{2} \] is $ Q(5, b, c) $, then $ a^2 + b^2 + c^2 $ is equal to

Find the point on the line $ \frac{x-1}{3} = \frac{y+1}{2} = \frac{z-4}{3} $ at a distance of $ \sqrt{2} $ units from the point $ (-1, -1, 2) $.

Find the foot of the perpendicular drawn from the point $ (1, 1, 4) $ on the line $ \frac{x+2}{5} = \frac{y+1}{2} = \frac{z-4}{-3} $.

Find the point on the line $ \frac{x-1}{3} = \frac{y+1}{2} = \frac{z-4}{3} $ at a distance of $ \sqrt{2} $ units from the point $ (-1, -1, 2) $.

The distance of the point $ P(-3,4,5) $ from the yz-plane is:

If a point $ P(x, y) $ satisfies the condition that its distance from the point $ (3, -2) $ is equal to its distance from the line $ y = 2x + 1 $, then the locus of point $ P $ is:

Find the midpoint of the line segment joining the points (3, 4) and (7, -2).

Find the distance between the points $ (2, 3) $ and $ (5, 7) $ in the Cartesian plane.

If the mirror image of the point $P(3,4,9)$ in the Line
$\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-2}{1}$ is $(α,β,γ)$ then find $14(a+ẞ+y)$ is:

If $x^2-y^2+2hxy+2gx+2fy+c=0$ is the locus of points such that it is equidistant from the lines $x+2y-8=0$ and $2x+y+7=0$, then value of $g+c+h-f$ is

If $ (a, b) $ be the orthocenter of the triangle whose vertices are $ (1, 2) $, $ (2, 3) $, and $ (3, 1) $, and $ I_1 = \int_a^b x \sin(4x - x^2) dx $, $ I_2 = \int_a^b \sin(4x - x^2) dx $, then $ 36 \frac{I_1}{I_2} $ is equal to:

If the line segment joining the points $ (1,0) $ and $ (0,1) $ subtends an angle of $ 45^\circ $ at a variable point $ P $, then the equation of the locus of $ P $ is:

Let the point $P(\alpha, \beta)$ be at a unit distance from each of the two lines $L _1: 3 x -4 y +12=0$, and $L _2: 8 x +6 y +11=0$ If $P$ lies below $L _1$ and above $L _2$, then $100(\alpha+\beta)$ is equal to

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line $$ 4x - 5y = 20 $$ to the circle $$ x^2 + y^2 = 9 \text{ is:} $$

A normal is drawn at the point $ P $ to the parabola $ y^2 = 8x $, which is inclined at $ 60^\circ $ with the straight line $ y = 8 $. Then the point $ P $ lies on the straight line:

In an isosceles triangle ABC, the vertex A is $(6, 1)$ and the equation of the base BC is $2x + y = 4$. Let the point B lie on the line $x + 3y = 7$. If $(α, β)$ is the centroid of ΔABC, then $15(α + β)$ is equal to :