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The equation of the tangent to the ellipse  at x = 3 is:

  1. 5x ± 3y = 25
  2. 3x ± 5y = 25
  3. 3x ± 5y = 16
  4. 5x ± 3y = 16

Answer (Detailed Solution Below)

Option 2 : 3x ± 5y = 25
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Detailed Solution

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Concept:

Tangent to an Ellipse:

The equation of the tangent to the ellipse , at a point (x1, y1), is given by: .

Calculation:

At x = 3, we will have:

⇒ 

⇒ y = ± 

From the above formula, we can say that the required equation of the tangent to the ellipse  at  and  are (respectively):

⇒

⇒ 3x + 5y = 25

OR

⇒ 

⇒ 3x - 5y = 25

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