The equation of the point's trajectory $y$ as a function of $x$ is

y = - \frac{x^{3} b}{a^{2}}

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y = - \frac{x^{2} b}{a^{3}}

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y = - \frac{x^{2} b}{a^{2}}

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y = - \frac{x b}{a^{2}}

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Solution

The correct option is D $y = - \frac{x^{2} b}{a^{2}}$
Given,
$y = - b t^{2}$ and $x = a t$
Now,
$y = - b t^{2}$
Multiply and divide RHS by $a^{2} t^{2}$ i.e. $x^{2}$
which gives us
$y = \frac{- b x^{2}}{a^{2}}$

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y (x)

The equation of the circle with center (– a, – b) and radius √a² – b² is:

x^{2} + y^{2} = c

Find the orthogonal trajectory of $x^{2} + y^{2} = c$

A_{1}, A_{2},

A_{3}

R^{2}

A_{1} = {(x, y) : x \geq 0, y \geq 0, 2 x + 2 y - x^{2} - y^{2} > 1 > x + y}, A_{2} = {(x, y) : x \geq 0, y \geq 0, x + y > 1 > x^{2} + y^{2}}, A_{3} = {(x, y) : x \geq 0, y \geq 0, x + y > 1 > x^{3} + y^{3}} .

| A_{1} |, | A_{2} |,

| A_{3} |

A_{1}, A_{2}

A_{3}

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