Question

If the parabola \[ y^{2}=9x \] cuts the ellipse \[ \frac{x^{2}}{9}+\frac{y^{2}}{b}=1 \] orthogonally, then the length of the latus rectum of the given parabola is

• A. \(2b\)
• B. \(\dfrac{b}{2}\)
• C. \(b\)
• D. \(\dfrac{b}{3}\)

Hint:

For two curves intersecting orthogonally, \[ \boxed{m_1m_2=-1.} \] Also, for the parabola \[ y^{2}=4ax, \] the length of the latus rectum is \[ \boxed{4a.} \]

Answer 1

The Correct Option is B