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If the distance between two parallel tangents having slope `m` drawn to the hyperbola `(x^2)/9-(y^2)/(49)=1` is 2, then the value of `2|m|` is_____

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The correct Answer is:
A
According to the question,
`(2sqrt(9x^(2)-49))/(sqrt(1+m^(2)))=2`
`"or "9x^(2)-49=1+m^(2)`
`"or "8x^(2)=50`
`"or "m=pm(5)/(2)`
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CENGAGE PUBLICATION-HYPERBOLA-EXERCISES
  1. The angle between the lines joining the origin to the points of inters...

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  2. A variable chord of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(b > a), s...

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  3. If the distance between two parallel tangents having slope m drawn to ...

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  4. If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , t...

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  5. A tangent drawn to hyperbola x^2/a^2-y^2/b^2 = 1 at P(pi/6) froms a t...

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  6. The number of roots of the equation x^2+5x+6=0 is

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  7. The locus of a point whose chord of contact with respect to the circle...

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  8. The sides A Ca n dA B of a A B C touch the conjugate hyperbola of the...

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  9. The number of possible tangents which can be drawn to the curve 4x^2-9...

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  10. The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 pa...

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  11. Locus of the feet of the perpendiculars drawn from either foci on a va...

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  12. P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, and N...

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  13. The coordinates of a point on the hyperbola (x^2)/(24)-(y^2)/(18)=1 wh...

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  14. The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 me...

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  15. The locus of a point, from where the tangents to the rectangular hyp...

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  16. If tangents P Qa n dP R are drawn from a variable point P to thehyperb...

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  17. The number of points on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 from w...

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  18. If a ray of light incident along the line 3x+(5-4sqrt(2))y=15 gets ref...

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  19. The chord of contact of a point P w.r.t a hyperbola and its auxiliary ...

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  20. The ellipse 4x^2+9y^2=36 and the hyperbola a^2x^2-y^2=4 intersect at r...

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