Question

I've tried doing this question but have only had little luck
http://i.imgur.com/AJO5MlT.png
I know that P = (a, 0), Q = (0, b)
And that squareroot(a^2+b^2)=squareroot of 45
But I don't know how to carry on.

Answer 1

sinx + cosx =1 I wonder if your x/a and y/b are sin and cos functions?

Answer 2

No I'm pretty sure they're not this is a coordinate geometry question I believe

Answer 3

Rule #1 - Keep Reading! You have not yet used all the given information!

You have the "Intercept Form". This is very nice. This resulted in the intercepts (a,0) and (0,b)

With the Distance, we have \(a^{2} + b^{2} = 45\)

With the Gradient of -1/2, we have \(\dfrac{b-0}{0-a} = -\dfrac{b}{a} = -\dfrac{1}{2}\)

That seems like enough information.

Answer 4

So do I then simultaneously solve it?

Answer 5

That would be an excellent idea.

Answer 6

b=3 and a=6
Thank you soo much for your help! :)

Answer 7

How did you rule out the fake answer?

Answer 8

Fake answer?
not sure what you mean...
I cross multiplied the gradient one and inputted substituted a into the first equation

Answer 9

Rule #1 - Never say "cross multiply" or you will offend me. (Not really, but pretty close.)

The gradient information suggests a = 2b

Substituting into the distance information: (2b)^2 + b^2 = 4b^2 + b^2 = 5b^2 = 45

b^2 = 9

b = +3 OR -3

For b = +3, we have a = +6
For b = -3, we have a = -6

Do they both meet the requirements of the problem statement?

Answer 10

Yes but in the question it says that a and b are positive constants.
And sorry about the 'cross multiply' lol

Answer 11

Perfect!!! See the value of reading the problem statement carefully and making sure your drag out of it ALL the pertinent information? Very good work.

Answer 12

Thanks so much for your help!!!