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Conic Sections

Parabolas, ellipses, and hyperbolas, oh my! Learn about this eccentric bunch of shapes.

Conics - Circle General Equation

What is the equation of the circle that passes through the origin, has its center on the line $$x+y=4,$$ and cuts the circle $$x^2+y^2-6x+16y+24=0$$ orthogonally?

Find the sum of all possible values of $$b$$ such that the two points $$(4, 0 )$$ and $$(- 4, 0)$$ lie on the circle $$x^2 + y^2 + ax + by +c =0$$ with radius $$6$$ .

If the line $$y=ax+b$$ cuts the circle $$x^2+y^2-4x+8y-29=0$$ into two equal parts, then what is the value of $$2a+b ?$$

If the circle $x^2+y^2+ax+by+c=0$ passes through three points $(-1,-8), (2,1), (6,-1),$ what is the value of $$a+b+c ?$$

If the circle $$x^2+y^2+Ax+By+C=0$$ passes through the origin and has the same center as the circle $$x^2+y^2-9x+8y-3=0,$$ what is the value of $$A+B+C?$$

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