question_answer 51)

Find the points on the curve x2 + y2 – 2x – 3 = 0 at which the tangent are parallel to X-axis. 

Answer:

Given curve is x2 + y2 ? 2x ? 3 = 0           ?.. (1)        Let P (h, k) be a pointy on (1)             Diff. (1) w.r.t. x                         m = slope of tangent to (1)             Now tangent is || X-axis        m = 0               (2)       K2 = 4             Required points are (1, 2), (1, ?2).