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Q)

Trace the curve y2(2a-x)=x3

Trace the curve y2(2a-x)=x3

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A)

. Symmetry: The curve is symmetrical about the x-axis.
{only even powers of 'y' occur in the equation}

2. Origin : The curve passes through the origin.
{ there is no constant term in its equation.}
The tangents at the origin are y = 0, 
{y = 0 equating to zero the lowest degree terms}
Origin is a cusp.

3. Asymptotes : The curve has an asymptote x = 2a.
{Co-eff. of y3 is absent, Co-eff. of y2 is an asymptote.}

4. Points : (a) curve meets the axes at (0,0) only.
(b) y2 = x3/(2a-x)

When x is - ve, y2 is - ve (y is imaginary) so that no portion of the curve lies to the left of the y-axis. Also when x> 2a, y2 is again-ve, so that no portion of the curve lies to the right of the line 3x = 2a.

 

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