Question

Trace the curve 9ay^2 =(x-2a)(x-5a)^2​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The curve $9ay^2=(x-2a)(x-5a)^2$ is traced for $-5\leq a\leq 5$.

Step-by-step explanation:

Consider the curve as follows:

$9ay^2=(x-2a)(x-5a)^2$, where $a$∈$R$.

Case1. For $a=-5$. The curve becomes

$9(-5)y^2=(x-2(-5))(x-5(-5))^2$

⇒ $-45y^2=(x+10)(x+25)^2$

⇒ $y^2=-\frac{(x+10)(x+25)^2}{45}$

The curve lies on negative $x-$axis.

Case2. For $a=0$. The curve becomes

$9(0)y^2=(x-2(0))(x-5(0))^2$

⇒ $0=(x)^3$

⇒ $x^3=0$

The curve at $a=0$ is a straight line lies on $y-$axis.

Case3. For $a=5$. The curve becomes

$9(5)y^2=(x-2(5))(x-5(5))^2$

⇒ $45y^2=(x-10)(x-25)^2$

⇒ $y^2=\frac{(x-10)(x-25)^2}{45}$

The curve lies on positive $x-$axis.

Notice that the curve moves from left to right as the value of $a$ increases.

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