List of top Mathematics Questions on Coordinate Geometry

The shortest distance between the lines $\frac{x−1}2 =\frac{y−2}1 =\frac{z−6}{-3} $ and $\frac{x−1}2 =\frac{y+8}{-7} =\frac{z−4}{5} $ is

Area bounded by larger part in I quadrant by x = 4y² , x = 2 and y = x is A then 3A equals

A line is cutting x axis and y axis at two points A and B, respectively, where OA = a, OB = b. A perpendicular is drawn from O (origin) to AB at an angle of $\frac{\pi}{6}$ from positive x-axis. If area of triangle OAB = $\frac{98\sqrt3}{3}$ sq. units, then $\sqrt3$ a + b is equal to

If the line $l_1 : 3y - 2x = 3$ is the angular bisector of the lines $l_2 : x - y + 1 = 0$ and $l_3$ : $αx + βy + 17 = 0$, then $α^2 + β^2 - α - β$ is equal to__

Let the line passing through the points P (2, –1, 2) and Q (5, 3, 4) meet the plane x – y + z = 4 at the point R. Then the distance of the point R from the plane x + 2y + 3z + 2 = 0 measured parallel to the line $\frac{x-7}{2}=\frac{y+3}{2}=\frac{z-2}{1}$ is equal to

Let P be the plane passing through the points (5, 3, 0), (13, 3, –2) and (1, 6, 2). For α ∈ N, if the distances of the points A (3, 4, α) and B (2, α, a) from the plane P are 2 and 3 respectively, then the positive value of a is

Find the circumradius if 2 is the side of the triangle with the opposite angle $\frac{\pi}{3}$.

S1 and S2 are two straight-line reflections of S1 in S2 and S2 in S1 coincide. Find the angle between both

When two straight-line reflections, S1 and S2, coincide, it implies that they are mirror images of each other with respect to a common line. In other words, S1 is a reflection of S2 and S2 is a reflection of S1, resulting in an overlap of their positions. In such a scenario, the angle between them is 0 degrees, meaning they are aligned perfectly.

$4x^2+hxy+y^2$ = 0 represent coincident lines. Find h = ?

What can be said regarding a line if its slope is negative?

Let a triangle be bounded by the lines L₁ : 2x + 5y = 10; L₂ : –4x + 3y = 12 and the line L₃, which passes through the point P(2, 3), intersects L₂ at A and L₁ at B. If the point P divides the line-segment AB, internally in the ratio 1 : 3, then the area of the triangle is equal to

A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x – y + 4 = 0, then the area of R is ________.

Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle, Then the area of ΔPQR is

Let image of point(8,5,7) with respect to line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{5}$ is (α,β,γ). Then, α+β+γ is equal to______.

A ray of light passing through (1, 2) after reflecting on x-axis at point Q passes through R(3, 4). If S(h, k) is such that PQRS is a parallelogram, then find the value of hk².

If the orthocentre of triangle formed by (8, 3), (5, 1) and (h, k) is (6, 1), then (h, k) lie on

The locus of P such that the ratio of distance P from A(3, 1) and B(1, 2) is 5 : 4 is