Question

A point P moves so that the sum of its distances from $(-ae,\,0)$ and $(ae,\,0)$ is $2a$ . Then the locus of P is

• A. $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1$
• B. $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1$
• C. $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}(1+{{e}^{2}})}=1$
• D. $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{a}^{2}}(1+{{e}^{2}})}=1$

Answer 1

Answer: (B)

$\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1$

Answer 2

By using the properties, the sum of focal distance of any points on the ellipse is equal to the major axis. $\therefore$ Required equation is $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1$