Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

Trace the curve : $y^{2}(2+x)=x^{2}(6-x)$

Can you answer this question?

1 Answer

0 votes
  • The strategies for curve tracing
  • (1) Domain-The values of x for which the function is defined
  • (2)Extent -Horizontal (vertical ) extent is determined by the intervals for $x(y)$ for which the curve exists
  • (3) $x=0$ gives the y intercept and y=0 gives the x -intercept
  • (4) If $(0,0)$ satisfies the equation, the curve passes through the orgin
  • (5) Find out whether the curve is symmetrical about any line. The curve is symmetric about
  • (i) x-axis if the equation is unaltered when y is replaced by -y
  • (ii) y-axis if the equation is unaltered when x is replaced by -x
  • (iii)the orgin if the equation is unattened when x is replaced by -x abd y by -y
  • (iv) the line $y=x$ if the equation is uttered when x and y are interchanged
  • (v) the line $ y=-x$ if the eauation is unchanged if x and y are replaced by -y and -x
  • (6) Asymptotes ($\parallel$ to coordinate axes)
  • If $y \to c$ (finite) when $x \to \pm \infty$
  • (or $ x \to k $ (finite ), when $y \to \pm \infty$
  • (7)Monotsnicity : Determine the intervals for which the curve is increasing or decreasing, using the first derivative test
  • (8) Special points: Determine the intervals of concavity/convexity and the points of inflection, using the second derivative test.
Step 1:
or $y^2=\large\frac{x^2(6-x)}{(2+x)}$
Step 2:
Existence : The curve is not defined for $x > 6$ and $x \leq -2$. so it lies in the interval $ -2 < x \leq 1$
Step 3:
(ii) Symmetry: The curve is symmetric about the x-axis only
Step 4:
(iii) Asymptotes: $x=-2$ is a vertical asymplote to the curve , parallel to the y-axis
Step 5:
The curve passes through $(0,0)$ twice $(6,0)$ once, and hence a loop is forward between $(0,0)\;and \; (6,0)$
answered Aug 19, 2013 by meena.p
Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App