Question

In which ratio does (-4,6) divides the line segment AB, from A(6-10) , B( 3,-8)​

Answer 1

GIVEN

In which ratio does (-4,6) divides the line segment AB, from A(6-10) , B( 3,-8)​

ANSWER

Given equation is $3x^{2}$+10xy+$3Y^{2}$ $3Y^{2}$    +16y+k=0

Comparing it with $Ax^{2}$+2hxy+$BY^{2}$+2gx+2fy+c=0

We get, a=3,h=5,b=3,g=0,f=8,c=k

The equation represents pair of straight lines.

∴  abc+2fgh−$AF^{2}$−$BG^{2}$−$CH^{2}$=0

⇒  3×3×k+2×8×0×5−$3(8) ^{2}$−$3(0)^{2}$−k$(5) ^{2}$=0

2:7

Therefore, the point C(−4,6) divides the line segment joining the points A(−6,10) and B(3,−8)in the ratio 2:7 internally.