Question

help with systems of conics!! please :)
[image attached]

Answer 1

What is your question?

Answer 2

What is the solution of the system?

Answer 3

the problem is in the picture is attached

Answer 4

@eliassaab

Answer 5

These are two cirlces

Answer 6

Yes I need to find what points they intersect at @eliassaab

Answer 7

OK

Answer 8

take their difference:$$x^2+y^2+4x+6y+12-(x^2+y^2+2x+2y)=0\\4x+6y+12-2x-2y=0\\2x+4y+12=0\\x+2y=-6$$now substitute \(x=-2y-6\) into either conic equation and solve for \(y\) to determine the intersection points

Answer 9

in other words the circles intersect along \(x+2y=-6\):

Answer 10

subtract the two equations
and then you will get a linear relation between x and y
use this to explictly express x in terms of y or y in terms of x and use substituition and any one of the equation method to solve the resulting quadratic equation..
to get two points of intersection if any

Answer 11

ergo$$x^2+y^2+2x+2y=0\\(-2y-6)^2+y^2+2(-2y-6)+2y=0\\4y^2+24y+36+y^2-4y-12+2y=0\\5y^2+22y+24=0$$

Answer 12

this is reducible; notice \(5\cdot24=120\) and clearly \(12\cdot10=120\) while \(12+10=22\)

Answer 13

Copy and paste in your browser the following link
http://www.wolframalpha.com/input/?i=Solve [+x^2+%2B+y^2+%2B+2+x+%2B+2+y+%3D%3D+0+%26%26++x^2+%2B+y^2+%2B+4+x+%2B+6+y+%2B+12+%3D%3D+0]

Answer 14

so$$5y^2+12y+10y+24=y(5y+12)+2y(5y+12)=(5y+12)(y+2)=0$$therefore \(y\in\{-2,-12/5\}\)

Answer 15

To check the above posts which are the right way to do the problem by hand

Answer 16

for \(y=-2\) we get \(x=-2(-2)-6=4-6=-2\) therefore \((-2,-2)\) is a point of intersection

for \(y=-12/5\) we get \(x=-2(-12/5)-6=24/5-30/5=-6/5\) so \((-6/5,-12/5)\) is another point

Answer 17

look at the pretty drawing: http://www.wolframalpha.com/input/?i=x%5E2++%2B+y%5E2+%2B+4x+%2B+6y+%2B+12+%3D+0%2C+x%5E2+%2B+y%5E2+%2B+2x+%2B+2y+%3D+0%2C+x+%2B+2y+%2B+6+%3D+0+for+-5+%3C%3D+x+%3C%3D+2

Answer 18

you can see how the line passes right thru the intersection

Answer 19

analytic geometry is beautiful

Answer 20

omg thank you so much @oldrin.bataku