Let a right angled triangle has vertices A and B

Question

Let a right angled triangle has vertices A and B on x axis and y axis and also vertex C with right angle is away from origin also AB = 5 , AC=4 and BC=3, then find locus of C if AB slides on coordinate axes.

Mssr Saketh · Accepted Answer

| | C Given AB=5 | /| B |\ / | BC=3 | \ / | AC=4 | \ / | –----------------------------------------|---- \/------|--------------------------- Let O be the origin O | A M LO = LM = 90o | | | | |As AB = 5 then as AOB is right angled triangle The values of OB and OA muust be equal to either of themLet OB = 3,OA = 4As A and B lie on X and Y axes respectively A(4,0) B(0,3)Let C(x,y) from given values they satisfy pythagoras theorem Therefore LA = 90o from A(4,0) B(0,3) C(x,y)BC = 3 AC = 4 _________ \/x2 + (y-3)2 = 3 => x2 + y2 – 6y + 9 => 9 x2+y2-6y=0---------(1) __________\/(x-4)2 + y2 = 4 => x2 -8x + 16 + y2 = 16 x2+y2-8x = 0-------------------(2) add Eq 1 and 2(1)+(2) --------------------------2x2 + 2y2 – 8x – 6y = 0 =>| x2 + y2 – 4x – 3y =0 | ---------------------------

Analytical Geometry> Let a right angled triangle has vertices ...

Let a right angled triangle has vertices A and B on x axis and y axis and also vertex C with right angle is away from origin also AB = 5 , AC=4 and BC=3, then find locus of C if AB slides on coordinate axes.

Aryan Kumar , 8 Years ago

Mssr Saketh

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Analytical Geometry> Let a right angled triangle has vertices ...

Let a right angled triangle has vertices A and B on x axis and y axis and also vertex C with right angle is away from origin also AB = 5 , AC=4 and BC=3, then find locus of C if AB slides on coordinate axes.

Aryan Kumar , 8 Years ago

Mssr Saketh

LIVE ONLINE CLASSES

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