Question

The total number of points on the curve x² - 4y² = 1 at which the tangents to the curve are parallel to the line x = 2y is ______.

Options

• 0

• 1

• 2

• 4

Answer 1

The total number of points on the curve x² - 4y² = 1 at which the tangents to the curve are parallel to the line x = 2y is 0.

Explanation:

Given equation of curve is

x² - 4y² = 1     ...(i)

Slope of tangent to the curve is

`dy/dx=x/(4y)`

Slope of line is x = 2y is `1/2`

Since the tangent is parallel to the given line,

`x/(4y)=1/2`

∴ x=2y

Substituting x = 2y in equation (i), we get

(2y)² - 4y² = 1

⇒ 0 = 1, which is not possible.

∴ The tangent is parallel to curve at zero point.