(B) Given the parametric equations: $x = \frac{2at}{1+t^2}$ $y = \frac{a(1-t^2)}{1+t^2}$ Substitute $t = \tan \theta$: $x = a \sin 2\theta$ $y = a \co

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(B) Given the parametric equations: $x = \frac{2at}{1+t^2}$ $y = \frac{a(1-t^2)}{1+t^2}$ Substitute $t = \tan \theta$: $x = a \sin 2\theta$ $y = a \cos 2\theta$ Squaring and adding both equations: $x^2 + y^2 = a^2 \sin^2 2\theta + a^2 \cos^2 2\theta$ $x^2 + y^2 = a^2(\sin^2 2\theta + \cos^2 2\theta)$ $x^2 + y^2 = a^2$ This is the equation of a circle with radius $a$. Therefore,$a$ is the radius of a circle.

Class 11 Mathematics 10-1.Circle and System of Circles Equations of circle

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If $x = \frac{2at}{1+t^2}$ and $y = \frac{a(1-t^2)}{1+t^2}$,where $t$ is a parameter,then $a$ represents:

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A
the length of the latus rectum of a parabola
B
the radius of a circle
C
the length of the transverse axis of a hyperbola
D
the length of the semi-major axis of an ellipse

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10-1.Circle and System of Circles

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Equations of circle

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DifficultJEE MAIN 2024

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MediumMHT CET 2020

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If $x = \frac{2at}{1+t^2}$ and $y = \frac{a(1-t^2)}{1+t^2}$,where $t$ is a parameter,then $a$ represents:

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