# Some problems with conic sections

1. Dec 18, 2009

### Mspike6

Here are some conic questions that am having problems with :

1) The general form of a particular ellipse is show Below. If the conic is translated 2 units left and 1 unit down, determine the new general term.

2x2+y2-2x+3y-9=0

2) Find the equation of a hyperbola in standard form or general form, that has its centre at (-2, 5), one vertex at (-2, 10), and the slope of one of its asymptotes is 5/4 .

2. Dec 18, 2009

### rl.bhat

Re: Conics

The standard equation of ellipse becomes
(x - 1/2)^2/(47/8) + (y-3/2)^2/(47/4) = 1

3. Dec 19, 2009

### chaoseverlasting

Re: Conics

Whats the question?

4. Dec 19, 2009

### Mspike6

Re: Conics

Sorry, i meant to ask if what i did is correct , or is there something am missing ?

5. Dec 20, 2009

### HallsofIvy

Staff Emeritus
Re: Conics

There is no need to convert to standard form. "Translating 2 units left" is exactly the same as adding 2 to x. "Translating one unit down" is exactly the same as subtracting 1 from y. Replace x by x+2 and y by y- 1.

Rotating through an angle $\theta$ gives $x'= x cos(\theta)+ y sin(\theta)$, $y'= x sin(\theta)- y cos(\theta)$. Replace x by $x cos(\theta)+ y sin(\theta)$, y by $x sin(\theta)- y cos(\theta)$. $\theta= arctan(5/4)$.

6. Dec 20, 2009

### Mspike6

Re: Conics

Thanks alot ! :D
really appreciate it