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Show that the point (x,y) given by x = (...

Show that the point (x,y) given by `x = (2at)/(1 + t^(2)) and y = (a(1-t^(2)))/(1+t^(2))` lies on a circle for all real values of t such that `-1 lt t lt 1` where a is any given real numbers.

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The correct Answer is:
`a^(2)`
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KUMAR PRAKASHAN-CONIC SECTIONS-SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (SHORT ANSWER TYPE QUESTIONS)
  1. Find the equation of the circle which touches the both axes in first q...

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  2. Show that the point (x,y) given by x = (2at)/(1 + t^(2)) and y = (a(1-...

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  3. IF a circle passes through the point (0,0) (a,0),(0,b) then find the ...

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  4. Find the equation of the circle which touches X - axis and whose centr...

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  5. If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a cir...

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  6. Find the equation of a circle which touches both the axes and the line...

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  7. If one end a diameter of the circle x^(2) + y^(2) - 4x - 6y + 11 = 0 i...

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  8. Find the equation of the circle having (1, -2) as its centre and passi...

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  9. Find k if line y = sqrt(3)x + k touches the circle x^(2) + y^(2) = 16.

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  10. Find the equation of a circle concentric with the circle x^(2) + y^(2)...

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  11. If the latus rectum of an ellipse is equal of half of minor axis, then...

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  12. Eccentricity of ellipe 9x^(2) + 25y^(2) = 225 is …….

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  13. If the eccentricity of an ellipse is (5)/(8) and ht distance between i...

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  14. …….is the equation of ellipse with eccentricity e = (2)/(3). Length of...

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  15. Find the distance between the directrices of th ellipse (x^(2))/(36) +...

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  16. Find the co-ordinates of a point on the parabola y^(2) = 8x whose foca...

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  17. Find the length of the line-segment joining the vertex of the parabola...

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  18. If the point (0,4) and (0,2) are respectively the vertex and focus of ...

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  19. If the line y = mx + 1 is tangent to the parabola y^(2) = 4x then find...

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  20. If the distance between the foci of a hyperbola is 16 and its eccentr...

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