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Find the equations of the tangents to the hyperbola `(x ^(2))/(a ^(2)) - (y ^(2))/( b ^(2)) = 1 ` are mutually perpendicular, show that the locus of P is the circle `x ^(2) + y ^(2) =a ^(2) -b ^(2).`

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The correct Answer is:
`x + y pm 1 =0`
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ICSE-HYPERBOLA -EXERCISE 25 (B)
  1. Find the tangent to the y ^(2) = 16x, making of 45 ^(@) with the x-axi...

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  2. A tangent to the parabola y^(2)=16x makes an angle of 60^(@) with the ...

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  3. Find the equations of the tangents to the parabola y ^(2) = 6x which p...

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  4. Find the equations of the tangents of the parabola y ^(2) + 12 x =0 fr...

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  5. Show that the line 12 y - 20 x -9=0 touches the parabola y ^(2) = 5x.

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  6. Show that the line x + y = 1 touches the parabola y = x-x ^(2).

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  7. Show that the line x + ny + an ^(2) =0 touches the parabola y ^(2) = 4...

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  8. Find the tangents to the ellipse x ^(2) + 9y ^(2) = 3, which are (i) p...

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  9. Find the equations of the tanggents to the ellipse (x ^(2))/(2) + (y ^...

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  10. Find the equation of the tangents of the ellipse (x ^(2)) /(16) + (y ^...

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  11. Find the value of 'c' so that 2x - y + c=0 may touch the ellipse x ^(2...

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  12. Show that the line lx + my = 1 will touch the ellipse (x ^(2))/( a ^(2...

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  13. Show that the line are tangent to the given hyperbolas and dectermine ...

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  14. Show that the line are tangent to the given hyperbolas and determine t...

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  15. Find the equations of the tangents to the hyperbola (x ^(2))/(a ^(2))...

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  16. Show that the straight line x + y=1 touches the hyperbola 2x ^(2) - 3y...

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  17. Find the equations of the tangents to the hyperbla 4x ^(2) - 9y ^(2) =...

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