Question

If the tangent at \( P(1, 1) \) on \( y^2 = x(2 - x) \) meets the curve again at \( Q \), then \( Q \) is:

• A. (2, 2)
• B. (−1, −2)
• C. \( \left( \frac{9}{4}, \frac{3}{8} \right) \)
• D. None of these

Hint:

To find the second intersection point of a tangent with a curve, use the point-slope form of the equation and solve for the coordinates.

Answer 1

The Correct Option is C

To find the point \( Q \), we need to find the equation of the tangent to the curve at \( P(1, 1) \). Using the point-slope form of the line and substituting the values of the curve, we find that the coordinates of \( Q \) are \( \left( \frac{9}{4}, \frac{3}{8} \right) \).

Step 2: Conclusion.
Thus, the correct answer is \( \left( \frac{9}{4}, \frac{3}{8} \right) \).