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Question

What is the nature of the curve $$5{x}^{2}+7y=0$$ 


Solution

The equation of the given curve is
$$F\left(x,y\right)=5{x}^{2}+7y=0$$
Here $$F\left(x,-y\right)=5{x}^{2}+7\left(-y\right)=5{x}^{2}-7y\neq F\left(x,-y\right)$$
$$F\left(-x,y\right)=5{\left(-x\right)}^{2}+7y=5{x}^{2}+7y=0=F\left(x,y\right)$$
$$F\left(-x,-y\right)=5{\left(-x\right)}^{2}+7\left(-y\right)=5{x}^{2}-7y\neq F\left(x,y\right)$$
$$\therefore\,$$ the given curve is symmetrical about the $$y-$$axis but neither about $$x-$$axis nor about the origin.

Mathematics

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