how to find the second point of intersection
how do you find the second point of intersection of a line through a circle given the equation of the circle the line and one set of coordinates? thanks
Original post by madfish
how do you find the second point of intersection of a line through a circle given the equation of the circle the line and one set of coordinates? thanks
simultaneous equations
the line with the curve
you will get a quadratic but you already know one root
Original post by madfish
how do you find the second point of intersection of a line through a circle given the equation of the circle the line and one set of coordinates? thanks
Either solve it simultaniously or know it will be on the opposite side of the center.
Original post by TenOfThem
simultaneous equations
the line with the curve
you will get a quadratic but you already know one root
the line with the curve
you will get a quadratic but you already know one root
i get a quadratic with 2 squared terms... y^2 and x^2
how do i solve that?
Original post by madfish
i get a quadratic with 2 squared terms... y^2 and x^2
how do i solve that?
how do i solve that?
simultaneously
you have another equation that says y=
From the equations of a straight line and a circle, substitute the line into the circle:
Then expand:
Group like terms, rearrange into the form and then substitute into the quadratic formula.
That gives you your two values of x, and y = mx + c lets you find the two corresponding values of y.
Unparseable latex formula:
y = mx + c[br]\\[br](x-a)^2 + (y-b)^2 = r^2[br]\\(x-a)^2 + (mx + c - b)^2 = r^2
Then expand:
Group like terms, rearrange into the form and then substitute into the quadratic formula.
That gives you your two values of x, and y = mx + c lets you find the two corresponding values of y.
(edited 11 years ago)
Original post by TenOfThem
simultaneously
you have another equation that says y=
you have another equation that says y=
so I solve by substitution then? I was setting both to zero and equating
Original post by madfish
so I solve by substitution then? I was setting both to zero and equating
yes, substitution
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