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The co ordinates of any position of a moving point P are given by

$$\left[\frac{(7t-2)}{(3t+2)} , \frac{(4t+5)}{(t-1)}\right]$$

where $t$ is a variable parameter.Find the equation of locus of $P$.

I could not understand the question especially saying what is a variable parameter. So please solve the question explaining the meaning of variable parameter

Hosein Rahnama
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Ger Wyn
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1 Answers1

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Say the co-ordinates of a point P is given by $(h,k)$. Then by the problem, $$h=\frac{7t-2}{3t+2}$$ $$k=\frac{4t+5}{t-1}$$ On simplification they give $$t=\frac{2+2h}{7-3h}$$ $$t=\frac{k+5}{k-4}$$

So required locus is $$\frac{2+2h}{7-3h}=\frac{k+5}{k-4}$$ i.e. $$\frac{2+2x}{7-3x}=\frac{y+5}{y-4}$$

Simplify to get your answer.

As for variable parameter, it is a something on which $x$ and $y$ depend, as you can see. So it is more fundamental. You might want to read this.

SchrodingersCat
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