I need help with my math question, can you try to explain how to do it please?

Question

Find the relationship relating x and y if C is the point (1,7), D is the point (1,13), Q is the point with coordinates (x,y), we know that
abs(DQ)=2*abs(CQ).

Answer 1

|DQ| = 2|CQ|
Thus DQ² = 4CQ²
On number plane d² = (x1 - x2)² + (y1 - y2)²

DQ² = (x - 1)² + (y - 13)² = x² - 2x + 1 + y² - 26y + 169
CQ² = (x - 1)² + (y - 7)² = x² - 2x + 1 + y² - 14y + 49
So 4CQ² = 4x² - 8x + 4y² - 56y + 200

Thus C follows the path:
x² - 2x + y² - 26y + 170 = 4x² - 8x + 4y² - 56y + 200

ie 3x² - 6x + 3y² - 30y + 30 = 0

ie x² - 2x + y² - 10y + 10 = 0
ie x² - 2x + 1 + y² - 10y + 25 = 16
ie (x - 1)² + (y - 5)² = 4²

This is a circle centre (1, 5) radius 4

Answer 2

As always, drawing a graph helps, but I'll see if I can get my message through with words alone.

CD is 6 long (easy to see on a graph), so if C,D and Q are colinear, CQ is 2 and DQ is 4. In this case x is 1, and y is 9. If we say that x is 2, then the distance from Q to C is SQRT((y-7)^2+1), and the distance from Q to D is SQRT((13-y)^2+1). Your calculator should be able to work out the value of y.
Now if we generallize the formulae, CQ's length is SQRT((y-7)^2+(1-x)^2) and DQ's length is SQRT((13-y)^2+(1-x)^2). Shove these into that last equation in your question, and relate away!

Edited to correct my sucky arithmatic. The easy stuff is too hard!

Answer 3

It is a simple example of geometry. Find the length of DQ and CQ then use the condition to get a quadratic relationship as follows:
x**2+5y**2-10y-2x-39=0

Answer 4

Q = (1, 9), (1, 1)

That's the easiest solution...There is curve
(x - 1)^2 + (y - 13)^2 = 4(x-1)^2 + 4(y-7)^2
(y - 13)^2 - 4(y-7)^2 = 3(x-1)^2
y^2 -26y + 169 - 4(y^2 -14y +49)
-3y^2 + 30y -27 = 3(x-1)^2
-(y^2 -10y +9) = -(y-9) (y-1) = (x - 1)^2
sqrt(-(y-9)(y-1)) + 1 = x valid only for y = from 1 to 9

Answer 5

sure and no. yet greater often than not no. Maths is almost a language. this is slightly different from English or chinese language or French or Latin, in that it has in simple terms summary ideas like variables and factors, strains and spheres, and a few issues like tesseracts and different multi-dimensional ideas. in actuality, ordinary language bargains with nouns and movements and modifiers of nouns (like adjectives) and verbs. arithmetic as a language is greater approximately ideas and operators. regardless of if, very almost each and every little thing in easy language could be broken down into ideas and operators. arithmetic isn't oftentimes used to describe issues like "pink" or why something strikes, because of the fact those at the instant are not abstractions. it extremely is utilized that way, with an exceptionally severe diploma of precision, a precision it incredibly isn't available in easy language. It additionally takes so a lot greater artwork (attempt) to realize this, on the grounds which you pay for the precision via that attempt. organic arithmetic is greater effective than in simple terms technology; this is, because of the fact the music places it "a variety of magic", it is why so few people get entangled with it for a lot greater effective than counting and straightforward math.

Answer 6

-(x-1)^2=(y-9)*(y-1)
u can use the equation adn recieve to ur answer
CQ=sqrt((x-1)^2+(y-7)^2)
DQ=sqrt((x-1)^2+(y-13)^2)
2*CQ=DQ
=> 4*CQ^2=DQ^2 :
4*((x-1)^2+(y-7)^2)=(x-1)^2+(y-13)^2
=>-3(x-1)^2=4*(y-7)^2-(y-13)^2
=>....
=>-(x-1)^2=(y-9)*(y-1)