Q.7 A rod of length 1.2m moves with its ends always touching the coordinate axes. The locus of a point P on the rod, which is 0.3m from the end in contact with x-axis is an ellipse. Find the eccentricity.

$f (x) = \{\begin{matrix} \frac{\sin (a + 1) x + \sin x}{x}, f o r x < 0 \\ x, f o r x = 0 \\ \frac{\sqrt{x + b x^{2}} - \sqrt{x}}{b x^{\frac{3}{2}}}, f o r x > 0 \end{matrix}$

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Q.7 A rod of length 1.2m moves with its ends always touching the coordinate axes. The locus of a point P on the rod, which is 0.3m from the end in contact with x-axis is an ellipse. Find the eccentricity.

f(x)=sina+1x+sinxx, for x<0x, for x=0x+bx2-xbx32, for x>0

$f (x) = \{\begin{matrix} \frac{\sin (a + 1) x + \sin x}{x}, f o r x < 0 \\ x, f o r x = 0 \\ \frac{\sqrt{x + b x^{2}} - \sqrt{x}}{b x^{\frac{3}{2}}}, f o r x > 0 \end{matrix}$