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From the point (2, 2) tangent are drawn ...

From the point (2, 2) tangent are drawn to the hyperbola `(x^2)/(16)-(y^2)/9=1.` Then the point of contact lies in the (a)first quadrant (b) second quadrant (c)third quadrant (d) fourth quadrant

A

first quadrant

B

second quadrant

C

third quadrant

D

forth quadrant

Text Solution

Verified by Experts

The correct Answer is:
C, D
The equations of asymptotes are `4y-3x=0 and 4y+3x=0`

As point (2, 2) lies above the asymptote, the points of contact of the tangents are in the third and fourth quadrants.
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Statement 1 : If from any point P(x_1, y_1) on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, then the corresponding chord of contact lies on an other branch of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola.

From any point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=2. The area cut-off by the chord of contact on the asymptotes is equal to a/2 (b) a b (c) 2a b (d) 4a b

(-2,3) lies in the II quadrant.

CENGAGE-HYPERBOLA-Exercise (Multiple)
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  2. The equation (x-alpha)^2+(y-beta)^2=k(l x+m y+n)^2 represents a parabo...

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  3. If (5,12)a n d(24 ,7) are the foci of a hyperbola passing through the ...

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  4. Show that the equation 9x^2-16 y^2-18 x+32 y-151=0 represents a hyperb...

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  5. If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)...

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  6. If the foci of (x^2)/(a^2)-(y^2)/(b^2)=1 coincide with the foci of (x^...

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  7. The differential equation (dy)/(dx)=(3y)/(2x) represents a family of h...

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  8. The is a point P on the hyperbola (x^(2))/(16)-(y^(2))/(6)=1 such that...

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  9. A parabola is drawn with focus at one of the foci of the ellipse (x^2)...

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  10. For which of the hyperbolas, can we have more than one pair of perpe...

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  11. The lines parallel to the normal to the curve x y=1 is/are (a)3x+4y+5=...

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  12. From the point (2, 2) tangent are drawn to the hyperbola (x^2)/(16)-(y...

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  13. For the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , let n be the number of p...

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  14. If the normal at P to the rectangular hyperbola x^2-y^2=4 meets the ax...

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  15. Find the equation of tangent to the hyperbola y=(x+9)/(x+5) which pas...

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  16. Tangents which are parrallel to the line 2x+y+8=0 are drawn to hyperb...

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  17. Find the equations of the tangents to the hyperbola x^2=9y^2=9 that ar...

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  18. Circle are drawn on the chords of the rectangular hyperbola x y=4 para...

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