Find the equation of the curve for which the normal at any point (x, y) passes through the origin. The curve represents a :

ellipse

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rectange

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circle

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hyperbola

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Solution

The correct option is D circle
The equation of the normal at any point $(x, y)$ of the curve is
$\frac{d y}{d x} (Y - y) + (X - x) = 0$
Since the required curve passes through origin
$\frac{d y}{d x} (0 - y) + (0 - x) = 0 \Rightarrow 2 (- y) d y + 2 (- x) d x = 0$
Integrating $x^{2} + y^{2} = c$

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Find the equation of the curve for which the normal at any point (x, y) passes through the origin. The curve represents a :

The correct option is D circleThe equation of the normal at any point (x,y) of the curve is dydx(Y−y)+(X−x)=0Since the required curve passes through origindydx(0−y)+(0−x)=0⇒2(−y)dy+2(−x)dx=0Integrating x2+y2=c

The correct option is D circle
The equation of the normal at any point $(x, y)$ of the curve is
$\frac{d y}{d x} (Y - y) + (X - x) = 0$
Since the required curve passes through origin
$\frac{d y}{d x} (0 - y) + (0 - x) = 0 \Rightarrow 2 (- y) d y + 2 (- x) d x = 0$
Integrating $x^{2} + y^{2} = c$