Question

A rod of length 2a slides with its ends on the axes the locus of the triangle of the circumcentre of triangle OPQ is

Answer 1

Answer:

Given length of rod=2a

Given length of rod=2aIt slides on axis.

Given length of rod=2aIt slides on axis.Let at a instant the coordinates of end of rods are (x,0) and (0,y)

Given length of rod=2aIt slides on axis.Let at a instant the coordinates of end of rods are (x,0) and (0,y)It is making a right angle triangle with origin

Given length of rod=2aIt slides on axis.Let at a instant the coordinates of end of rods are (x,0) and (0,y)It is making a right angle triangle with originHere length of hypotenuse =2a

Given length of rod=2aIt slides on axis.Let at a instant the coordinates of end of rods are (x,0) and (0,y)It is making a right angle triangle with originHere length of hypotenuse =2aBy Pythagoras theorem,

Given length of rod=2aIt slides on axis.Let at a instant the coordinates of end of rods are (x,0) and (0,y)It is making a right angle triangle with originHere length of hypotenuse =2aBy Pythagoras theorem,x2+y2=(2a)2

Given length of rod=2aIt slides on axis.Let at a instant the coordinates of end of rods are (x,0) and (0,y)It is making a right angle triangle with originHere length of hypotenuse =2aBy Pythagoras theorem,x2+y2=(2a)2x2+y2=4a2 ……….(1)

Given length of rod=2aIt slides on axis.Let at a instant the coordinates of end of rods are (x,0) and (0,y)It is making a right angle triangle with originHere length of hypotenuse =2aBy Pythagoras theorem,x2+y2=(2a)2x2+y2=4a2 ……….(1)As it is a right angle triangle circumcircle of ΔOXY is the mid point of hypotenuse (2x,2y)

Given length of rod=2aIt slides on axis.Let at a instant the coordinates of end of rods are (x,0) and (0,y)It is making a right angle triangle with originHere length of hypotenuse =2aBy Pythagoras theorem,x2+y2=(2a)2x2+y2=4a2 ……….(1)As it is a right angle triangle circumcircle of ΔOXY is the mid point of hypotenuse (2x,2y)∴x=2x,y=2y

Given length of rod=2aIt slides on axis.Let at a instant the coordinates of end of rods are (x,0) and (0,y)It is making a right angle triangle with originHere length of hypotenuse =2aBy Pythagoras theorem,x2+y2=(2a)2x2+y2=4a2 ……….(1)As it is a right angle triangle circumcircle of ΔOXY is the mid point of hypotenuse (2x,2y)∴x=2x,y=2yx=2x y=2y

Given length of rod=2aIt slides on axis.Let at a instant the coordinates of end of rods are (x,0) and (0,y)It is making a right angle triangle with originHere length of hypotenuse =2aBy Pythagoras theorem,x2+y2=(2a)2x2+y2=4a2 ……….(1)As it is a right angle triangle circumcircle of ΔOXY is the mid point of hypotenuse (2x,2y)∴x=2x,y=2yx=2x y=2ySubstitute in (1)

Given length of rod=2aIt slides on axis.Let at a instant the coordinates of end of rods are (x,0) and (0,y)It is making a right angle triangle with originHere length of hypotenuse =2aBy Pythagoras theorem,x2+y2=(2a)2x2+y2=4a2 ……….(1)As it is a right angle triangle circumcircle of ΔOXY is the mid point of hypotenuse (2x,2y)∴x=2x,y=2yx=2x y=2ySubstitute in (1)(2x)2+(2y)2=4a2

Given length of rod=2aIt slides on axis.Let at a instant the coordinates of end of rods are (x,0) and (0,y)It is making a right angle triangle with originHere length of hypotenuse =2aBy Pythagoras theorem,x2+y2=(2a)2x2+y2=4a2 ……….(1)As it is a right angle triangle circumcircle of ΔOXY is the mid point of hypotenuse (2x,2y)∴x=2x,y=2yx=2x y=2ySubstitute in (1)(2x)2+(2y)2=4a24[x2+y2]=4a2

Given length of rod=2aIt slides on axis.Let at a instant the coordinates of end of rods are (x,0) and (0,y)It is making a right angle triangle with originHere length of hypotenuse =2aBy Pythagoras theorem,x2+y2=(2a)2x2+y2=4a2 ……….(1)As it is a right angle triangle circumcircle of ΔOXY is the mid point of hypotenuse (2x,2y)∴x=2x,y=2yx=2x y=2ySubstitute in (1)(2x)2+(2y)2=4a24[x2+y2]=4a2x2+y2=a.

Step-by-step explanation:

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