Problem involving Locus

[mathangel]

PQ is 5metres long and R is a point on PQ such that RQ is 2 times RP. Find:
(a) the locus of point R when the ladder PQ slides down the wall,
(b) the coordinates of point R when it touches the floor.

?((a-0)^2+(0-b)^2 )=25
From this equation,
I can get a = 0 and a = 10 and b = 5.

RQ = 2RP

Although I have all these information, I still can’t get the final answer (36x^2+9y^2-100=0).
Is there any mistake in the information? Or how should I continue from here?

 

[Deleted member 4993]

PQ is 5metres long and R is a point on PQ such that RQ is 2 times RP. Find:
(a) the locus of point R when the ladder PQ slides down the wall,
(b) the coordinates of point R when it touches the floor.

?((a-0)^2+(0-b)^2 )=25
From this equation,
I can get a = 0 and a = 10 and b = 5.

RQ = 2RP

Although I have all these information, I still can’t get the final answer (36x^2+9y^2-100=0).
Is there any mistake in the information? Or how should I continue from here?

P
|\
| \
|  \
S   *R
|    \
|     \
|      \
--------
O   T    Q

Let PO and OQ be the wall

Let mPQO = ?

and co-ordinate of R(x,y)

then

RP = x*sec?
RQ = y * cosec?

RQ/RP = 2 = y/x * cot?

tan? = y/(2x)

sin? = y/?(y² + 4x²)

cos? = 2x/?(y² + 4x²)

Then we have

TQ/RT = cot?

(5cos? - x)/y = cot?

5/y * [2x/?(y² + 4x²)] - x/y = 2x/y

10*x/?(y² + 4x²) = 3x

and simplify further.....

 

[Denis]

10*x/?(y² + 4x²)] = 3x

Be advised that your bracketing is erroneous; you need a serious talk with your teacher :shock: