Question

The points on the curve `x^2/9 + y^2/25 = 1`, where tangent is parallel to X-axis are ______.

Options

• (±5, 0)

• (0, ±5)

• (0, ±3)

• (±3, 0)

Answer 1

The points on the curve `x^2/9 + y^2/25 = 1`, where tangent is parallel to X-axis are (0, ±5).

Explanation:

The equation of the given curve:

`x^2/9 + y^2/25 = 1`

On differentiating both sides w.r.t. x, we get

`(2x)/9 + (2y)/25 dy/dx = 1`

`\implies dy/dx = (-25x)/(9y)`

Since the tangent is parallel to the X-axis, the slope is zero.

∴ `(-25)/9 x/y = 0`, which is possible if x = 0

Put x = 0 in equation (i), we get

`y^2/25 = 1`

`\implies` y² = 25

`\implies` y = ±5

Hence, required points are (0, ±5).