Question

eliminate the arbitrary constants and form corresponding partial differential equation ax^2+by^2+cz^2=1

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Answer 1

Answer:

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Answer 2

Answer:

The solution for the partial differentatial equation is $x=\sqrt{\frac{1-b y^{2}-c z^{2}}{a}}, x=-\sqrt{\frac{1-b y^{2}-c z^{2}}{a}}$

Step-by-step explanation:

Here we have given equatrion $a x^{2}+b y^{2}+c z^{2}=1$

Subtract $b y^{2}+c z^{2}$From both sides

$a x^{2}+b y^{2}+c z^{2}-\left(b y^{2}+c z^{2}\right)=1-\left(b y^{2}+c z^{2}\right)$

Simplify

$a x^{2}=1-\left(b y^{2}+c z^{2}\right)$

Divide both sides by $a ; \quad a \neq 0$

Simplify

$x^{2}=\frac{1-b y^{2}-c z^{2}}{a} ; \quad a \neq 0$

For $x^{2}=f(a)$

The solutions are $x=\sqrt{f(a)},-\sqrt{f(a)}$

$x=\sqrt{\frac{1-b y^{2}-c z^{2}}{a}}, \\x=-\sqrt{\frac{1-b y^{2}-c z^{2}}{a}} ; \quad a \neq 0$