Perpendicular distance problem

[Dumbledore211]

Homework Statement

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

Homework 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

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

 

[Tanya Sharma]

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

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 N^r as well as D^r .Eliminating the common factor will give you the desired result .

 

[Mark44]

Homework Statement

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

Homework 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

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:
$$Ax1+By1 + \frac{C}{\sqrt{A^2 + B^2}}$$

The Attempt at a Solution

One question is when we multiply two quantities having absolute value signs doesn't it become a whole square??

Not in general.
|a||b| ≠ ab, if that's what you're asking.

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