Questions
A ladder of length ‘a’ rests against the floor and a wall of a room. If the ladder begins to slide on the floor, then the locus of its middle point is
a
x2 + y2 = a2
b
2(x2 + y2) = a2
c
x2 + y2 = 2a2
d
4(x2 + y2) = a2
detailed solution
Correct option is D
Let AB be the ladder. Let the cross section of the floor and wall be taken as the coordinates axes. Let P(x, y) be the mid-point of AB whose locus is required. Then the coordinates of A and B are (2x, 0) and (0, 2y) respectively.Given, AB = a⇒2x-02+0-2y2=a⇒4x2+4y2=a2or 4(x2 + y2) = a2, which is the required locusTalk to our academic expert!
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A line L cuts the sides AB, BC of ABC in the ratio 2 : 5, 7 : 4 respectively. Then the line L cuts CA in the ratio
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