A straight line is such that the portion of it intercepted between the axes is bisected at the point `(x_1,y_1)`. Prove that its equation is `(x)/(x_1) + y/(y_1) = 2`.

A line is such that its segment between the lines 5x-y+4=0 and 3x+4y-4=0 is bisected at the point (1,5). Obtain its equation.

Find the equation of the tangent to the curve x^2/a^2-y^2/b^2=1 at the point (x_1,y_1)

Find the equation of the straight line, which passes through the point (1, 4) and is such that the segment of the line intercepted between the axes is divided by the point in the ratio 1: 2.

Prove that the line through the point (x_1,y_1) and parallel to the line Ax + By + C = 0 is A (x- x_1) + B (y -y_1) = 0.

Prove that the line through the point (x_(1),y_(1)) and parallel to the line Ax+By+C=0 is A(x-x_(1)) +B(y-y_(1))=0 .

The equation of the straight line which bisects the intercepts between the axes of the lines x+y=2 and 2x + 3y = 6 is

The condition on a and b , such that the portion of the line a x+b y-1=0 intercepted between the lines a x+y=0 and x+b y=0 subtends a right angle at the origin, is a=b (b) a+b=0 a=2b (d) 2a=b

Find the equations of the tangent line to the curve: y = 2x^2 + 3y^2 = 5 at the point (1,1)

Find the product of the perpendiculars drawn from the point (x_1,y_1) on the lines ax^2+2hxy+by^2=0

The equation of the bisector of that angle between the lines x + y = 3 and 2x - y = 2 which contains the point (1,1) is