Question

The point on the ellipse \(\frac{x^{2}}{25}+\frac{y^{2}}{9}=1\) which is equidistant from its foci can be

• A. \((0,3)\)
• B. \((5,0)\)
• C. \((3,0)\)
• D. \((0,5)\)

Hint:

Such a point lies on the perpendicular bisector of the foci, which is the minor axis.

Answer 1

The Correct Option is A

Step 1: Test the options
The foci are $(\pm 4,0)$.
$(0,5)$ does not lie on the ellipse.

Step 2: Check (0,3)
Distance to $(4,0)$: $\sqrt{16+9}=5$.
Distance to $(-4,0)$: $5$. Equal, and $(0,3)$ lies on the ellipse.

Step 3: Other points
$(\pm5,0)$ and $(3,0)$ are not equidistant from the foci.

Final Answer:
Only (0, 3) is on the ellipse and equidistant from the foci. \[ \boxed{\text{(A) }(0,3)} \]