Question

The area of the quadrilateral formed by the common tangents drawn to the circle \[ x^2+y^2=16 \] and the ellipse \[ 7x^2+25y^2=175 \] is:

• A. \(64\)
• B. \(32\)
• C. \(5\sqrt2\)
• D. \(16\sqrt2\)

Hint:

For a tangent \(y=mx+c\) to the ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1, \] remember the condition \[ c^2=a^2m^2+b^2. \] Equating this with the tangency condition of another conic is often the fastest way to obtain common tangents.

Answer 1

The Correct Option is A