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The locus of a point P ( alpha , beta )...

The locus of a point ` P ( alpha , beta ) ` moving under the condition that the line ` y= alpha x + beta ` is a tangent to the hyperbola ` (x^(2))/(a^(2)) - (y^(2))/(b^(2))=1 ` is a/an-

A

parabola

B

hyperbola

C

circle

D

ellipse

Text Solution

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The correct Answer is:
B
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If a straight line passes through the point (alpha , beta) and the portion of the line intercepted between the axes is divided equally at that point , then (x)/(alpha) + (y)/(beta) is _

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CHHAYA PUBLICATION-MCQ ZONE 3 -Question Paper 6
  1. If the tangent to the curve y^(2) = x^(3) at the point (m^(2), m^(3)...

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  2. If A is the area of the region bounded by the curve y= sqrt(3x + 4) ,...

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  3. The locus of a point P ( alpha , beta ) moving under the condition t...

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  4. The curves y= sin x and y= cos x intersect infinitely many times g...

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  5. From a point (d, 0) three normals are drawn to the parabola y^(2)=x, t...

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  6. The condition that the line ax + by + c =0 is a tangent to the parab...

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  7. The normal to the curve x= a ( cos theta + theta sin theta ) , y= a( ...

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  8. If the tangent to the parabola y= x^(2) + 6 at the point (1, 7) also...

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  9. The parabolas y^(2)= 4x and x^(2) = 4y divide the square region boun...

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  10. The greatest value of the function f(x) = x^(2)"log" (1)/(x) is-

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  11. If f(x) = x^(3) - 6x^(2) + 9x +3 be a decreasing function, then x lie...

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  12. The minimum value of the function f(theta) = 6 cos theta + 8 sin theta...

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  13. The abscissa of the point on the parabola y^(2) = 2px which is neare...

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  14. The value of a for which the function (a+2)x^(3) - 3ax^(2) + 9ax -1 de...

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  15. A minimum value of the function f(x) = int(0)^(x) te^(-t^(2))dt is-

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  16. If f(x)= x^(3) + ax^(2) + bx + c is an increasing function for all re...

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  17. The area ( in square unit ) in the first quadrant bounded by the parab...

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  18. The slope of the tangent at (x, y) to a curve passing through (1, (pi...

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  19. The time rate of change of the radius of a sphere is (1)/(2 pi) . Whe...

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  20. The rate at which microbe multiply is proportional to the instantaneou...

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