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If values of a, for which the line y=ax+...

If values of a, for which the line `y=ax+2sqrt(5)` touches the hyperbola `16x^2-9y^2 = 144` are the roots of the equation `x^2-(a_1+b_1)x-4=0`, then the values of `a_1+b_1` is

A

2

B

4

C

zero

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
The equation of the hyperbola is
`(x^(2))/(9)-(y^(2))/(16)=1`
The equation of the tangent is
`y=mx+sqrt(9x^(2)-16)`
`"or sqrt(9m^(2)-16)=2sqrt5`
`"or "m= pm2`
or a + b = sum of roots = 0
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CENGAGE-HYPERBOLA-Exercise (Single)
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  9. P is a point on the hyperbola (x^(2))/(y^(2))-(y^(2))/(b^(2))=1, and N...

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  12. The locus of a point, from where the tangents to the rectangular hy...

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

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  14. The number of points on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=3 from w...

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

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

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

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  18. The locus of the point which is such that the chord of contact of t...

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  19. If x=9 is the chord of contact of the hyperbola x^2-y^2=9 then the equ...

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  20. If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2...

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