Question

A rod of length 12cm moves with its ends always touching the coordinates axis Determine the equation of the locus of P on the rod Which is 3cm from the end in contact with x axis( With Diagram)

Answer 1

Hey friend your answer is here


Given a rod of length 12 cm moves with its ends always touching the coordinate axes.

Again given a point P on the rod, which is 3 cm from the end in contact with the x-axis.

It is shown in the figure.



Here AP = 3 cm, AB = 12

Now BP = AB - AP

=> BP = 12 - 3

=> BP = 9 cm

Again from figure,

∠PAO = ∠BPO = θ    (since PQ || OA and are corresponding angles)

Now in ΔBPO,

cosθ = QP/BP

=> cosθ = x/9 .............1

Again in ΔPAr,

sinθ = PR/PA

=> sinθ = y/3 ........2

Now square equation 1 and 2 and then add them, we get

cos2 θ + sin2 θ = x2 /81 + y2 /9

=> x2 /81 + y2 /9 = 1      (since cos2 θ + sin2 θ = 1 )

So the equation of the locus of a point P is x2 /81 + y2 /9 = 1 

Answer 2

hey this is ur answer with attached photo may help u






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