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Find the locus of the third vertex of a ...

Find the locus of the third vertex of a right angled triangle , the ends of whose hypotenuse are (4,0) and (0,4)

Text Solution

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The correct Answer is:
`x^(2)+y^(2)-4x-4y=0`
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Find the the locus of the third vertex of a right angled triangle, the ends of whose hypotenuse are (4,0) and (0,4).

Show that in a right angled triangle, the hypotenuse is the longest side.

Knowledge Check

  • The maximum area of a right angled triangle with hypotenuse h is

    A
    `h^(2)//2 sqrt(2)`
    B
    `h^(2)//2`
    C
    `h^(2)//sqrt(2)`
    D
    `h^(2)//4`

  • If a right angled triangle is revolved about its hypotenuse then it will form a ………..

    A
    double cone
    B
    triple cone
    C
    only cone
    D
    none

  • The legs of a right triangle are a and b the linc segment of length d connecting the vertex of the right angle to a point P of the hypotenuse enclose an angle delta with the leg a. The quantities a, b, d and delta are correctly related as

    A
    `1/(2d) = (cos delta)/a + (sin delta)/b`
    B
    `2/d= (cos delta)/a + (sin delta)/b`
    C
    `1/d = (cos delta)/a + (sin delta)/b`
    D
    `2/d = (cos delta)/b + (sin delta)/a`

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    The ends of the hypotenuse of a right angle triangle are (0,6) and (6,0) . Find the equation of locus of its third vertex.

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