Distance of a Point From a Line

IMPORTANT

Distance of a Point From a Line: Overview

This topic covers concepts such as Distance between Two Parallel Lines, Perpendicular Distance of a Point from a Line, and Length of the Perpendicular from Origin to the Line.

Important Questions on Distance of a Point From a Line

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Find the length of perpendicular from origin to line 5x+12y=13

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Find the length of perpendicular from origin to line 5x+12y=8

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Find the length of perpendicular from origin to line 5x+12y-3=0

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Find the length of perpendicular from origin to line 3x+4y-3=0

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Find the length of perpendicular from origin to line 3x+4y+5=0

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The distance between the lines 4x+3y-11=0 and 8x+6y-15=0 is a10 units. Write the value of a.

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Let S be a subset of the plane defined by S=x,y:|x|+2|y|=1. Then, the radius of the smallest circle with centre at the origin and having non-empty intersection with S is

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The distance between the lines 3x+4y=9 and 6x+8y=15 (in units)  is equal to

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Consider the plane x+y-z=1 and point A(1,2,-3) . A line L has the equation x=1+3r, y=2-r & z=3+4r.

 The distance between the points on the line which are at a distance of 4 / 3   from the plane is

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Consider the triangle having vertices O0, 0, A2, 0 and B1, 3. Also bmina1, a2, a3 means ba1 when a1 is least ; ba2 when a2 is least and so on. From this we can say ba1, ba2, ........., ban .

Let R be the region consisting of all those points P inside Δ OAB which satisfy OPminBP, AP. Then the area of the region R is

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For next two question please follow the same

Consider the triangle having vertices O0, 0, A2, 0 and B1, 3. Also bmina1, a2, a3 means ba1 when a1 is least ; ba2 when a2 is least and so on. From this we can say ba1, ba2, ........., ban .

Let R be the region consisting of all those points P inside Δ OAB which satisfy d P, OA min [ d P, OB d P, AB ] , where d denotes the distance from the point to the corresponding line. Then the area of the regionaR is

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The lengths of the perpendiculars from the points m2,2m, mn,m+n and n2,2n to the line x+3y+3=0 are in

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What is the distance between the planes 3x+4y-7=0 and 6x+8y+6=0?

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The maximum possible length of semi latus rectum is

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The equation of the base of an equilateral triangle is x+y=2 and it's vertex is 2, -1. If the length of its equal side is 6 k , then the value of k is

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If an equilateral triangle, having centroid at the origin, has a side along the line x+y=2, then the area (in sq.units) of this triangle is

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The distance of the point -2,4,-5 from the line x+33=y-45=z+86 is

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A straight line passes through the points 5,0 and 0,3. The length of perpendicular form the point 4,4 on the line is

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The distance of the point P(a, b, c) from the x -axis is

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If A5,-4 and B7,6 are points in a plane, then the set of all points Px,y in the plane such that AP:PB=2:3 is