The equation of the tangents to the ellipse 4x² + 5y² = 20 which are perpendicular to line 3x + 2y - 5 = 0 is

Calculation:

The equation of the given ellipse is  4x2 + 5y2 = 20

It can be written as , which is comparable with the first standard form 

Here a² = 5 and b² = 4.

The given line is 3x + 2y - 5 = 0, its slope = -(3/2)

Since the tangents are perpendicular to the given line, the slope of the required tangents is 2/3 (from m₁ m₂ = -1)

Thus the equation of the required tangents is,

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Additional Information Tangents to an Ellipse:

→ If the line y = mx + c touches the ellipse , then c2 = a2m2 + b2.

→ The straight lines  represent the tangents to the ellipse.