Area of the triangle with vertices (a, b...

Area of the triangle with vertices (a, b) `(x_(1), y_(1))` and `(x_(2), y_(2))`, where `a, x_(1), x_(2)` are in GP. with common ratio r and `b, y_(1), y_(2)` are in GP. with common ratio s is :

`ab(r-1)(s-1)(s-r)`

`(1)/(2) ab(r+1)(s+1)(s-r)`

`(1)/(2)ab(r-1)(s-1)(s-r)`

`ab(r+1)(s+1)(r-s)`

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If the tangents at (x_(1),y_(1)) and (x_(2),y_(2)) to the parabola y^(2)=4ax meet at (x_(3),y_(3)) then

`x_(1),x_(2),x_(3)` are A.P

`x_(1),x_(3),x_(2)` are A.P

`y_(1),y_(2),y_(3)` are A.P

`x_(1),x_(2),x_(3)` are A.P

`sqrt((x_(1)+x_(2))^(2)+(y_(1)+y_(2))^(2))`

`sqrt((x_(1)+x_(2))^(2)+(y_(1)+y_(2)))^(2)`

`sqrt((x_(1)-x_(2))-(y_(1)+y_(2)))`

`sqrt((x_(1)-x_(2))^(2)+(y_(1)-y_(2))^(2))`

lie on a st. line

lie on an ellipse

lie on a circle

are vertices of a triangle