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Q.

The curve in which the slope of the tangent at any point equals the ratio of the abscissa to the ordinate of the point, is

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a

an ellipse

b

a rectangular hyperbola

c

a parabola

d

a circle

answer is C.

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Detailed Solution

We have,

$\frac{d y}{d x} = \frac{x}{y} \Rightarrow y d y = x d x \Rightarrow \frac{y^{2}}{2} = \frac{x^{2}}{2} - C$

$\Rightarrow y^{2} - x^{2} = 2 C$ , which is a rectangular hyperbola

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