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

Question

Jit Mitra · Answer

S = ax 2 +by 2 +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.

mukul kant · Answer

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

Jit Mitra · Answer

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.

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

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

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