A) touches X-axis
B) bisects the angle between the axes
C) makes an angle of \[60{}^\circ \] with OX
D) none of these
Correct Answer: B
Solution :
| \[{{y}^{2}}={{x}^{2}}\,(x+1),\] \[x+1\ge 0\] |
| \[y=\pm \,\,x\sqrt{x+1}\] |
| \[\therefore \] \[\frac{dy}{dx}=\pm \left( \sqrt{x+1}+\frac{x}{2\sqrt{x+1}} \right)\] |
| \[=\pm \,\,\frac{2\,(x+1)+x}{2\sqrt{x+1}}=\pm \,\,\frac{3x+2}{2\sqrt{x+1}}\] |
| \[\therefore \] \[\underset{x\,=\,0}{\mathop{\left. \frac{dy}{dx} \right|}}\,=\pm \,\,1\] |
| \[\therefore \] at (0, 0) the curve bisects the angle between the axes. |
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