Coordinate geometry in 2D and 3D — lines, conics, planes, spheres.
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Q1 · Analytical Geometry of Two and Three Dimensions · EASY
A line passes through the points (2, 3) and (5, 9). What is the slope of this line?
Q2 · Analytical Geometry of Two and Three Dimensions · MEDIUM
The equation of a circle is x^2 + y^2 - 6x + 4y - 12 = 0. What is the radius of this circle?
Q3 · Analytical Geometry of Two and Three Dimensions · EASY
The distance between the point (1, 2, 3) and the point (4, 6, 8) in 3D space is:
Q4 · Analytical Geometry of Two and Three Dimensions · MEDIUM
A line has direction ratios 2, -3, 6. What are the direction cosines of this line?
Q5 · Analytical Geometry of Two and Three Dimensions · HARD
The equation of a plane passing through the point (1, 2, 3) and perpendicular to the vector with direction ratios 4, -2, 1 is: