A common tangent to the parabola and the circle cuts the coordinate axes at two points. What is the area of the triangle formed by this tangent and the axes?

Answer and explanation

Correct answer: D. 9/2

**Why not the others: The value 9 forgets the factor in the right-triangle area formula, while other options result from incorrect slope derivations of the common tangent.
  1. Step 1: The equation of a tangent with slope to the parabola (where ) has standard form .
  2. Step 2: For this line to be tangent to the circle , the perpendicular distance from the center must equal the circle radius : .
  3. Step 3: Square both sides: . Factoring gives , so .
  4. Step 4: Taking , the tangent line is . The axes intercepts are and . The area of the right-angled triangle formed with the axes is .
Answer
9/2.

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