Grade 12Analytical Geometry
derivation (trick) for the point of intersection of a pair of straight lines with a curve (in 2 degree)
3 Answers
Jit Mitra
Approved Tutor Answer14 Years agoS = 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.
mukul kant
Any similar method (generic) for intersection of two curves/ a curve and a line?
Jit Mitra
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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