derivation (trick) for the point of intersection of a pair of straight lines with a curve (in 2 degree)


3 years ago

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                                        S = ax2+by2+2gx+2fy+2hxy+c = 0

Partially differentiate S w.r.t x and y respectively.

2ax + 2g + 2hy = 0
ax+hy+g = 0     ...............(i)

2by + 2f + 2hx = 0
by + hx + f = 0    ..............(ii)

Solve (i) and (ii) for x and y.

(x,y) is the point of intersection.

2 years ago
                                        Any similar method (generic) for intersection of two curves/ a curve and a line?

2 years ago
                                        This method isnt actually to find the intersection of two curves. This is used to find the centre of the curve. Incase of pair of straight lines, it is infact, the point of their intersection. In ellipse and hyperbola, u get the center.

2 years ago

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