Locus of foot of normal drawn from any focus to variable tangent of hyperbola 4x^2-9y^2-8x- 18y = 41

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10-2. Parabola, Ellipse, Hyperbola

normal

Locus of foot of normal drawn from any focus to variable tangent of hyperbola $4x^2-9y^2-8x- 18y = 41$ will be

A

$x^2 + y^2 - 2x + 2y = 3$

B

$x^2 + y^2 - 2x + 2y = 7$

C

$x^2 + y^2 = 9$

D

$x^2 + y^2 = 5$

Solution

Hyperbola is $ \frac{(x-1)^{2}}{9}-\frac{(y+1)^{2}}{4}=1$ ……..$(i)$

Required locus will be Auxiliary circle of $( i )$

$(x-1)^{2}+(y+1)^{2}=9$

Standard 11

Mathematics

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