The locus of the point of intersection of the lines x - a 1- t 2-1- t 2 and y -2 at -1- t 2 represents- t being a parameterA- a circle with a radius of a unitsB- a circle passing through originC- pair of lines passsing through a - a D- pair of lines passsing through 0-0

The correct option is A a circle with a radius of a unitsGiven, x=a ( 1 t^21+t^2 ) and y=2at1+t^2 ⇒ x^2+y^2=a^2((1 t^2)^2+4t^2(1+t^2)^2) ∴ x^2+y^2=a^2 Which r ...

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Byju's Answer

Standard XII

Mathematics

Parametric Equation of a Circle

The locus of ...

Question

The locus of the point of intersection of the lines $x = a (\frac{1 - t^{2}}{1 + t^{2}})$ and $y = \frac{2 a t}{1 + t^{2}}$ represents, $t$ being a parameter

a circle with a radius of

a

units

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a circle passing through origin

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pair of lines passsing through

(a, a)

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pair of lines passsing through

(0, 0)

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Solution

The correct option is A a circle with a radius of $a$ units
Given, $x = a (\frac{1 - t^{2}}{1 + t^{2}})$ and $y = \frac{2 a t}{1 + t^{2}}$
$\Rightarrow x^{2} + y^{2} = a^{2} (\frac{(1 - t^{2})^{2} + 4 t^{2}}{(1 + t^{2})^{2}})$
$∴ x^{2} + y^{2} = a^{2}$
Which represents a circle.

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The locus of the point of intersection of the lines x=a(1−t21+t2) and y=2at1+t2 represents, t being a parameter

The correct option is A a circle with a radius of a unitsGiven, x=a(1−t21+t2) and y=2at1+t2 ⇒x2+y2=a2((1−t2)2+4t2(1+t2)2) ∴ x2+y2=a2 Which represents a circle.

The locus of the point of intersection of the lines $x = a (\frac{1 - t^{2}}{1 + t^{2}})$ and $y = \frac{2 a t}{1 + t^{2}}$ represents, $t$ being a parameter

The correct option is A a circle with a radius of $a$ units
Given, $x = a (\frac{1 - t^{2}}{1 + t^{2}})$ and $y = \frac{2 a t}{1 + t^{2}}$
$\Rightarrow x^{2} + y^{2} = a^{2} (\frac{(1 - t^{2})^{2} + 4 t^{2}}{(1 + t^{2})^{2}})$
$∴ x^{2} + y^{2} = a^{2}$
Which represents a circle.