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Draw a sketch.Let B=(5,21), C=(40,14) and $\frac{BP}{PC}$=1/6. What is the most efficent way to find P? My book just states P=(6/7)B+(1/7)C but no idea how they got that.
If x and y are the coordinates of P, then it must be...Let B=(5,21), C=(40,14) and $\frac{BP}{PC}$=1/6. What is the most efficent way to find P? My book just states P=(6/7)B+(1/7)C but no idea how they got that.
'Monster Wolfram' says that the quadratic curve in this case is a circle...If x and y are the coordinates of P, then it must be...
$\displaystyle f(x,y)= 36\ (x5)^{2} + 36\ (y21)^{2}  (x40)^{2}  (y+14)^{2}=0$ (1)
The (1) is a 'quadratic curve' as illustrated in...
Quadratic Curve  from Wolfram MathWorld
Let $B=(5,21),\;C=(40,\text{}14),\;\dfrac{BP}{PC}=\dfrac{1}{6}$
What is the most efficent way to find $P$ ?

 (5,21) +35
 B♥ → → → → → → +
 * ↓
 Po ↓
 * ↓ 35
+*↓
 * ↓
 * ↓
 ♥C
 (40,14)

If your book gives that answer then you have not posted the question as asked, or omitted implied side conditions for the question set.Let B=(5,21), C=(40,14) and $\frac{BP}{PC}$=1/6. What is the most efficent way to find P? My book just states P=(6/7)B+(1/7)C but no idea how they got that.
Even though your problem is solved maybe you want to get some background information. If so have a look here: Circles of Apollonius  Wikipedia, the free encyclopediaI've solved this now thanks to the answers.