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# L1 is a tangent drawn to the curve x2−4y2=16 at A(5,32). L2 is another tangent parallel to L1 which meets the curve at B. L3 and L4 are normals to the curve at A and B respectively. Lines L1,L2,L3,L4 form a rectangle. Then

A
Equation of tangent at B is 6y=5x16.
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B
Equation of normal at B is 12x+10y+75=0.
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C
Radius of largest circle inscribed in the rectangle is 3261
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D
Radius of the circle circumscribing the rectangle is 1092
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Solution

## The correct option is D Radius of the circle circumscribing the rectangle is √1092x216−y24=1 (5,32) lies on the curve. Tangent at A: 5x16−32(y4)=1 ⇒L1:5x−6y=16 Tangent at B: L2:5x−6y=−16 Normal at A: 6x+5y=λ Normal passes through A(5,32) 30+152=λ⇒λ=752 L3:6x+5y=752 Similarly, normal at B is L4:6x+5y=−752 Distance between tangents 2r=32√25+36 ∴r=16√61 Radius of circumcircle of rectangle is R=√25+94=√1092  Suggest Corrections  0      Similar questions  Explore more