Question 554469
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hi, i need your help please... i don't know how to answer these questions because i can't fully imagine them... 
i hope you can help me because i really want to understand this lesson for the sake of my grades.....

(a) the sum of the distance from a point P to (4,0) and (-4,0) is 9. if the abscissa of P is 1, find its ordinate.

(b) the center of a circle is at (-3,-2). if a chord of length 4 is bisected at (3,1), find the length of the radius.
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        In the post by  @Theo,  problem  (b)  is solved incorrectly and his answer is wrong.

        I came to bring a correct solution.



<pre>
Let P = (-3,-2) be the center of the circle.

Let C = (3,1) be the midpoint of the chord.

Let point A be one of the intersections of the chord with the circle.


Triangle PCA is a right-angled triangle with right angle at vertex C.


The leg CA has the length of 4/2 = 2 units  (half the length of the chord).


The leg PC has the length  {{{sqrt((3-(-3))^2 + (1-(-2))^2)}}} = {{{sqrt(6^2 + 3^2)}}} = {{{sqrt(36+9)}}} = {{{sqrt(45)}}}.


Therefore the length of the radius, which is the hypotenuse PA of this right-angled triangle PCA, is


    r = |PA| = {{{sqrt( PC^2 + CA^2)}}} = {{{sqrt(45 + 4)}}} = {{{sqrt(49)}}} = 7.


<U>ANSWER</U>.  The radius is 7 units long.
</pre>

Solved correctly. 

The solution is short, straightforward and elegant - as it is should be for a Math problem.


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This problem is nice.  &nbsp;As &nbsp;I &nbsp;see, &nbsp;it is from a classic source and created by really qualified &nbsp;Math composer.


All input data is carefully selected and polished, &nbsp;so that the output is a round number.
This reveals a professional composer and a good source.