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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)

Grade:12

3 Answers

Jit Mitra
25 Points
9 years ago

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.

mukul kant
18 Points
9 years ago

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

Jit Mitra
25 Points
9 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.

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