There exists points on Cartesian coordinate. Point has coordinates . Point is on the origin .
Point and always has a constant distance of from each other.
Point moves with a horizontal velocity (parallel to the x-axis) of
Point moves with a horizontal velocity of
Point 's vertical velocity (parallel to the y-axis) is while Point is allowed to move vertically in order to keep the constant distance of .
All this movement is happening in the first quadrant.
Let be the area made by the figure defined by: the axis, the axis, and the path traveled by point up to where it meets the axis. Find
After you solve this, you might want to try a continuation of this problem.
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In the diagram above, ABCD and PQRS are both rectangles. Points P, Q, R, and S lie on segments , , , and , respectively, and .
If and , then the maximum possible value of can be written in the form , where . What is ?
Given line intersects circle at and . If is the origin and , what is the value of ?
Let two Rods of length and of length are sliding on smooth standard co-ordinate axis such that their ends are always con-cyclic. If the locus of centre of that circle which pass through all four points is expressed as:
For positive integers . What is the minimum value of
Details and Assumptions
Two lines pass through the point and each is a distance of 2 from the origin at their closest to the origin. What is the sum of the slopes of these lines?