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Question

The equations of the tangents to the ellipse 4x2+3y2=5 which are perpendicular to the line 3xy+7=0 are

A
2x2y±55=0
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B
2x12y±552=0
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C
2x+6y±65=0
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D
2x+2y±15=0
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Solution

The correct option is C 2x+6y±65=0
Equation of ellipse: x254+y253=1

Equation of line perpendicular to tangent: y=3x+7m1=3

Since lines are perpendicular m1×m2=1m2=13

Equation of tangent:

y=mx+a2m2+b2

y=(13)x+(54)(19)+(53)

3y+x3=656

2x+6y±65=0

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