# Thread: Standard Form of an Equation

1. ## Standard Form of an Equation

Write in standard form, the equation with integral coefficients for the set of coplanar points described. For each point, its distance from the fixed point $\displaystyle (-1,-2)$ is $\displaystyle \frac{1}{4}$ its distance from the fixed point $\displaystyle (6,-4)$.

Is this answer right - $\displaystyle 15x^2 + 15y^2 + 44x + 56y + 28 = 0$ ?

2. Let the point be (x,y).

We can use the distance formula.

$\displaystyle \sqrt{(x+1)^{2}+(y+2)^{2}}=\frac{1}{4}\sqrt{(x-6)^{2}+(y+4)^{2}}$

3. Originally Posted by galactus
Let the point be (x,y).

We can use the distance formula.

$\displaystyle (x+1)^{2}+(y+2)^{2}=\frac{1}{4}\left[(x-6)^{2}+(y+4)^{2}\right]$
Should't the equation be $\displaystyle (x+1)^{2}+(y+2)^{2}=\frac{1}{16}\left[(x-6)^{2}+(y+4)^{2}\right]$ instead. After your square both sides to get rid of the radical you also square $\displaystyle \frac {1}{4}$ to get $\displaystyle \frac {1}{16}$ and from there on solve. So is my answer right in my 1st post?

4. Yes, you're correct. I forgot to include my radical signs.

5. Originally Posted by galactus
Yes, you're correct. I forgot to include my radical signs.
Alright thnx. I just wanted to make sure I answered the equation right?