Question

The number of possible tangents which can be drawn to the curve 4x² – 9y² = 36, which are perpendicular to the straight line 5x + 2y – 10 = 0 is ______.

Options

• zero

• 1

• 2

• 4

Answer 1

The number of possible tangents which can be drawn to the curve 4x² – 9y² = 36, which are perpendicular to the straight line 5x + 2y – 10 = 0 is zero.

Explanation:

Given equation of curve: 4x² – 9y² = 36

⇒ `x^2/9 - y^2/4` = 1

Equation of straight line: 5x + 2y – 10 = 0

Slope of line perpendicular to it: `2/5`

For hyperbola, condition of tangency is c² = m²a² – b²

⇒ c² = `4/25 xx 9 - 4`

⇒ c² = `-64/5`

which is not possible

Hence, no tangents are possible to the given curve