The tangents from `(2,0)` to the curve `y=x^(2)+3` meet the curve at `(x_(1),y_(1))` and `(x_(2),y_(2))` then `x_(1)+x_(2)` equals

If the tangent at (x_(0),y_(0)) to the curve x^(3)+y^(3)=a^(3) meets the curve again at (x_(1),y_(1)) , then (x_(1))/(x_(0))+(y_(1))/(y_(0)) is equal to

The tangent to the curve y=e^(2x) at the point (0,1) meets X-axis at

If the tangent at (x_(1),y_(1)) to the curve x^(3)+y^(3)=a^(3) meets the curve again in (x_(2),y_(2)), then prove that (x_(2))/(x_(1))+(y2)/(y_(1))=-1

Through the focus of the parabola y^(2)=2px(p>0) a line is drawn which intersects the curve at A(x_(1),y_(1)) and B(x_(2),y_(2)). The ratio (y_(1)y_(2))/(x_(1)x_(2)) equals.-

The points on the curve f(x)=(x)/(1-x^(2)) , where the tangent to it has slope equal to unity, are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) . Then, x_(1)+x_(2)+x_(3) is equal to

The tangent to the curve y = e^(2x) at the point (0,1) meets x - axis at :