Question

The Y-intercept of the common tangent to the parabolas \(y^2=32 x\) and \(x^2=108 y\) is

• A. 3
• B. -12
• C. -3
• D. 2

Hint:

Write the tangent with slope m to each parabola and equate the two intercepts.

Answer 1

The Correct Option is B

Step 1: Check the Second Form
Intercept from the second parabola: $-27m^{2}=-27\cdot\dfrac{4}{9}=-12$.

Step 2: Same Value
Intercept from the first parabola: $\dfrac{8}{-2/3}=-12$.

Step 3: Conclusion
Both agree, so the intercept is $-12$, option (B).

Final Answer:
The common tangent cuts the y-axis at $-12$. \[ \boxed{\text{(B) }-12} \]