# Perpendicular distance problem

1. Jan 17, 2014

### Dumbledore211

1. The problem statement, all variables and given/known data

Show that the product of the perpendicular distance problems drawn from the points (√5, 0) and (-√5, 0) on the line 2xcosα-3ysinα=6 is independent of α

2. Relevant equations
Eqn of perpendicular distance Ax1+By1 + C/ (A^2 +B^2)^1/2 The whole formula will be within the absolute value sign. Sorry, I don't have the toolkit to use that sign at present

3. The attempt at a solution
One question is when we multiply two quantities having absolute value signs doesn't it become a whole square?? Anyway, how can I eliminate the coefficients like 2 and 3 within the square root thing so that we can rewrite the denominator expression as sin^2α + cos^2α=1. Do I use trig identities to get rid of α in the final expression

2. Jan 17, 2014

### Tanya Sharma

Do not think too far ahead .Why do you need to eliminate 2 and 3 ? Using the identity sin2α + cos2α=1 , eliminate sin2α from denominator .You will find something common in Nr as well as Dr .Eliminating the common factor will give you the desired result .

3. Jan 17, 2014

### Staff: Mentor

There's no toolkit - on a computer keyboard there is a | key above the backslash key. If you're doing this on a phone then you're handicapping yourself, IMO.

In any case, your expression (it's not an equation) for the perp. distance needs some grouping symbol for the numerator. Otherwise, here's what you wrote:
$$Ax1+By1 + \frac{C}{\sqrt{A^2 + B^2}}$$
Not in general.
|a||b| ≠ ab, if that's what you're asking.