Question

If the ends of the hypotenuse are (a,0) and (-a, 0), then the locus of the third vertex of the triangle 4
a) x2 - y2 = 2a
b) x2 - y2 = a? c) x2 + y2 = a
d) x² + y2 = 2a?
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Answer 1

Answer:

Explanation:

given A(a,0) and B(-a, 0)

let the third vertex be C(x,y)

according to Pythagoras theorem; $side^{2 }+side^{2} =hypotenuse^{2}$

---> $AC^{2}+BC^{2}=AB^{2}$ ---1

here AC square=

---> ($(\sqrt{(a-x)^{2}+(0-y)^{2} })^{2}$

---->$a^{2}+x^{2} -2ax+y^{2} }$

and$BC^{2}$=

--->$(\sqrt{(x+a)^{2}+(y-0)^{2} })^{2}$

---->$a^{2}+x^{2} +2ax+y^{2} }$

and $AB^{2}$=

----> $\sqrt{(a+a)^{2}+ 0 }$

--->$4a^{2}$

now substituting everything in 1 we get

$x^{2} +y^{2}= 2a^{2}$