Question

Que1 :-- If point ( x , y ) is equidistant from the point ( a+b , b-a ) & ( a-b , a+b then prove that bx = ay​

Answer 1

Answer:

If the point p(x y) is equidistant from a(a+b b-a) and b(a-b a+b), bx = ay proved.

Step-by-step explanation:

Given P(x, y) is equidistant from points A(a + b, b - a) and B(a - b, b + a).

To find, prove that bx = ay.

∴ PA^{2} =PB^{2}PA

2

=PB

2

Using distance formula,

\sqrt{(x_{2}- x_{1})^{2}+(y_{2}- y_{1})^{2}}

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

⇒{(a+b-x)^{2}+{(b-a-y)^{2}}={(a-b-x)^{2}+{(a+b-y)^{2}}

⇒{(a+b-x)^{2}-(a-b-x)^{2}={(a+b-y)^{2}-(b-a-y)^{2}

⇒(a+b-x+a-b-x)(a+b-x-a+b+x)=(a+b-y+b-a-y)(a+b-y-b+a+y)(a+b−x+a−b−x)(a+b−x−a+b+x)=(a+b−y+b−a−y)(a+b−y−b+a+y)

⇒ (2a-2x)(2b)=(2b-2y)(2a)(2a−2x)(2b)=(2b−2y)(2a)

⇒ (a-x)(b)=(b-y)(a)(a−x)(b)=(b−y)(a)

⇒ ab-bx=ab-ayab−bx=ab−ay

⇒bx=aybx=ay , proved.

Answer 2

Step-by-step explanation:

i hope it's helped you!!