Question-145202

Question Number 145202 by mnjuly1970 last updated on 03/Jul/21

Commented by loveineq last updated on 03/Jul/21

Wow, it likes a therom .

Answered by ajfour last updated on 03/Jul/21

{(x + 3 p)}^{2} + y^{2} = a^{2}

{(x + p)}^{2} + y^{2} = b^{2}

{(x - p)}^{2} + y^{2} = c^{2}

{(x + 3 p)}^{2} + y^{2} = d^{2}

a^{2} + 3 c^{2} = 4 x^{2} + 12 p^{2} + 4 y^{2}

d^{2} + 3 b^{2} = 4 x^{2} + 12 p^{2} + 4 y^{2}

h e n c e

a^{2} + 3 c^{2} = d^{2} + 3 b^{2}

Commented by mnjuly1970 last updated on 03/Jul/21

t h a n k y o u s o m u c h m r a j f o r

Answered by mr W last updated on 03/Jul/21

\frac{x^{2} + b^{2} - a^{2}}{2 x b} = - \frac{x^{2} + b^{2} - c^{2}}{2 x b}

\Rightarrow 2 x^{2} = a^{2} + c^{2} - 2 b^{2} \dots (i)

s i m i l a r l y

\Rightarrow 2 x^{2} = b^{2} + d^{2} - 2 c^{2} \dots (i i)

a^{2} + c^{2} - 2 b^{2} = b^{2} + d^{2} - 2 c^{2}

\Rightarrow a^{2} + 3 c^{2} = d^{2} + 3 b^{2}

Commented by mnjuly1970 last updated on 03/Jul/21

t h a n k a l o t m r W, v e r y n i c e

s o l u t i o n \dots