Question

समीकरणx² -y²= 2ay का ध्रुवीय निर्देशांक रूप लिखिए।​

Answer 1

Answer:

गणित में ध्रुवीय निर्देशांक पद्धति (polar coordinate system) द्विविमीय-निर्देशांक पद्धति है जिसमें किसी बिन्दु के निर्देशांक उस बिन्दु की किसी सन्दर्भ बिन्दु से दूरी एवं सन्दर्भ ...

Step-by-step explanation:

The polar coordinates r and ϕ can be converted to the Cartesian coordinates x and y by using the trigonometric functions sine and cosine:

{\displaystyle x=r\cos \varphi \,}{\displaystyle x=r\cos \varphi \,}

{\displaystyle y=r\sin \varphi \,}{\displaystyle y=r\sin \varphi \,}

The Cartesian coordinates x and y can be converted to polar coordinates r and ϕ with r ≥ 0 and ϕ in the interval (−π, π] by:[1]

{\displaystyle r={\sqrt {x^{2}+y^{2}}}\quad }{\displaystyle r={\sqrt {x^{2}+y^{2}}}\quad } (as in the Pythagorean theorem or the Euclidean norm), and

{\displaystyle \varphi =\operatorname {atan2} (y,x)\quad }{\displaystyle \varphi =\operatorname {atan2} (y,x)\quad },

where atan2 is a common variation on the arctangent function defined as

{\displaystyle \operatorname {atan2} (y,x)={\begin{cases}\arctan({\frac {y}{x}})&{\mbox{if }}x>0\\\arctan({\frac {y}{x}})+\pi &{\mbox{if }}x<0{\mbox{ and }}y\geq 0\\\arctan({\frac {y}{x}})-\pi &{\mbox{if }}x<0{\mbox{ and }}y<0\\{\frac {\pi }{2}}&{\mbox{if }}x=0{\mbox{ and }}y>0\\-{\frac {\pi }{2}}&{\mbox{if }}x=0{\mbox{ and }}y<0\\{\text{undefined}}&{\mbox{if }}x=0{\mbox{ and }}y=0\end{cases}}}{\displaystyle \operatorname {atan2} (y,x)={\begin{cases}\arctan({\frac {y}{x}})&{\mbox{if }}x>0\\\arctan({\frac {y}{x}})+\pi &{\mbox{if }}x<0{\mbox{ and }}y\geq 0\\\arctan({\frac {y}{x}})-\pi &{\mbox{if }}x<0{\mbox{ and }}y<0\\{\frac {\pi }{2}}&{\mbox{if }}x=0{\mbox{ and }}y>0\\-{\frac {\pi }{2}}&{\mbox{if }}x=0{\mbox{ and }}y<0\\{\text{undefined}}&{\mbox{if }}x=0{\mbox{ and }}y=0\end{cases}}}

The value of ϕ above is the principal value of the complex number function arg applied to x+iy. An angle in the range [0, 2π) may be obtained by adding 2π to the value in case it is negative.

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