Question

A curve is represented by the equation x = sec²t and y = cot t, where t is a parameter. If the tangent at the point P on the curve where t = `π/4` meets 4 the curve again at the point Q, then |PQ| is equal to ______.

Options

• `(5sqrt(3))/2`

• `(5sqrt(5))/2`

• `(2sqrt(5))/3`

• `(3sqrt(5))/2`

Answer 1

A curve is represented by the equation x = sec²t and y = cot t, where t is a parameter. If the tangent at the point P on the curve where t = `π/4` meets 4 the curve again at the point Q, then |PQ| is equal to `underlinebb((3sqrt(5))/2)`.

Explanation:

Eliminating t gives y² (x – 1) = 1.

Equation of the tangent at P(2, 1) is x + 2y = 4.

Solving with curve x = 5 and y = `–1/2`, we get

Q ≡ `(5, –1/2)` or PQ = `(3sqrt(5))/2`