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The x-intercept of the tangent at any ar...

The x-intercept of the tangent at any arbitrary point of the curve `a/(x^2)+b/(y^2)=1` is proportional to (a)square of the abscissa of the point of tangency (b)square root of the abscissa of the point of tangency (c)cube of the abscissa of the point of tangency (d)cube root of the abscissa of the point of tangency

A

square of the abscissa of the point of tangency

B

square root of the absciss of the point of tangency

C

cube of the abscissa of the point of tangency

D

cube root of the abscissa of the point of tangency

Text Solution

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The correct Answer is:
C
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CENGAGE-APPLICATION OF DERIVATIVES-Exercise (Single)
  1. The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tan...

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  2. Let C be the curve y=x^3 (where x takes all real values). The tangent ...

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  3. The x-intercept of the tangent at any arbitrary point of the curve a/(...

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  4. Given g(x)=(x+2)/(x-1) and the line 3x+y-10=0. Then the line is (a)tan...

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  5. The number of point in the rectangle {(x , y)}-12lt=xlt=12a n d-3lt=yl...

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  6. Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) ...

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  7. The line tangent to the curves y^3-x^2y+5y-2x=0 and x^2-x^3y^2+5x+2y=0...

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  8. The two curves x=y^2,x y=a^3 cut orthogonally at a point. Then a^2 is ...

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  9. The tangent to the curve y=e^(k x) at a point (0,1) meets the x-axis a...

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  10. The curves 4x^2+9y^2=72 and x^2-y^2=5a t(3,2) touch each other (b)...

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  11. The coordinates of a point on the parabola y^2=8x whose distance from ...

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  12. At the point P(a,a^(n)) on the graph of y=x^(n)(n in N) in the first q...

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  13. Let f be a continuous, differentiable, and bijective function. If the ...

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  14. A point on the parabola y^2=18 x at which the ordinate increases at tw...

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  15. Find the rate of change of volume of a sphere with respect to its s...

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  16. If there is an error of k % in measuring the edge of a cube, then the ...

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  17. A lamp of negligible height is placed on the ground l1 away from a wal...

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  18. The function f(x)=x(x+3)e^(-(1/2)x) satisfies the conditions of Rolle'...

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  19. The radius of a right circular cylinder increases at the rate of 0.1 ...

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  20. A cube of ice melts without changing its shape at the uniform rate ...

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