Question

Let y = f(x) be a curve whose parametric equation is

x = t² + t + 1, y = t² – t + 1; where t > 0. Total number of tangents that can be drawn to this curve from (1, 1) is/are equal to

• A. 1
• B. 2
• C. 3
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

$\frac { d y } { d x } = \frac { 2 t - 1 } { 2 t + 1 }$. Equation of tangent at point 't' is;

(y − (t² − t +1) = $\frac { 2 t - 1 } { 2 t + 1 }$ (x − (t² + t +1)).

If it passes through (1,1)

then, (2t + 1) (1 − (t² + t + 1)) = (2t − 1) (1 − (t² + t + 1))

⇒ t = 0

As t > 0. That means no tangent can be drawn.