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1. Hi, Can anyone please help me through this GCSE Maths question stage by stage with the working out cos I really don't know how to do it!!!

The straight line with the equation y=x+6 meets the circle with the equation x^2+y^2=50 at two points P and Q.

By solving two simutaneous equations, find the coordinates of P and Q.

(No graph paper provided btw)
2. (Original post by kieshaxxx)
Hi, Can anyone please help me through this GCSE Maths question stage by stage with the working out cos I really don't know how to do it!!!

The straight line with the equation y=x+6 meets the circle with the equation x^2+y^2=50 at two points P and Q.

By solving two simutaneous equations, find the coordinates of P and Q.

(No graph paper provided btw)
Sub all instances of y with x+6 therefore:

x^2+y^2=50 becomes x^2+(x+6)^2=50 expand and solve the quadratic.
3. When the line and the circle meet, they will have the same x and y co-ordinates so they are simultaneous equations. If you substitute the eqn of the line into the eqn of the circle, you get x^2 + (x+6)^2 = 50
x^2 + x^2 + 12x + 36 = 50
2x^2 + 12x - 14 = 0
x^2 + 6x - 7 = 0
(x+7)(x-1) = 0
So either x = 1 or x = -7
Substitute back into the equation of the line, at x = 1, y = 1+6=7, at x = -7, y = -7+6 = -1 so they meet at (1,7) and (-7,-1) You can check these points are right by making sure they lie on the circle (sub into left hand side, check the answer is 50)
4. (Original post by Bezza)
x^2 + (x+6)^2 = 50
x^2 + x^2 + 12x + 36 = 50
2x^2 + 12x - 14 = 0
x^2 + 6x - 7 = 0
(x+7)(x-1) = 0
So either x = 1 or x = -7
Substitute back into the equation of the line, at x = 1, y = 1+6=7, at x = -7, y = -7+6 = -1 so they meet at (1,7) and (-7,-1) You can check these points are right by making sure they lie on the circle (sub into left hand side, check the answer is 50)

I don't understand what you did after subbing the x+6 into the circle equation .... sorry I'm a bit slow when it comes to maths!
5. (Original post by kieshaxxx)
I don't understand what you did after subbing the x+6 into the circle equation .... sorry I'm a bit slow when it comes to maths!
Multiply out the brackets (x+6)^2 = (x+6)(x+6) = x^2 + 6x + 6x + 36 = x^2 + 12x + 36, then I just added on the other x^2 and took 50 away from both sides. As all the numbers are even you can divide by 2, then factorise the quadratic equation.
6. (Original post by Bezza)
Multiply out the brackets (x+6)^2 = (x+6)(x+6) = x^2 + 6x + 6x + 36 = x^2 + 12x + 36, then I just added on the other x^2 and took 50 away from both sides. As all the numbers are even you can divide by 2, then factorise the quadratic equation.
Ahhhh .... thankyou soooo much!!! I get it now, and it's easy oH and worth 5 marks! I could always do with an extra 5 marks!
7. (Original post by kieshaxxx)
Ahhhh .... thankyou soooo much!!! I get it now, and it's easy oH and worth 5 marks! I could always do with an extra 5 marks!

X² + Y² = 50 is a circle around the origin with radius √50.

And Y = X + 6 is just a straight line gradient one and y intercept 6.

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