Find the equation of the line which passes through `P(1,-7)` and meets the axes at A and B respectively so that `4A P-3B P=0.`

Find the equation of the line which passes through P(1,-7) and meets the axes at Aa n dB respectively so that 4A P-3B P=0.

Find the equation of straight line which passes through the point P(2,6) and cuts the coordinate axis at the point A and B respectively so that AP:BP=2:3.

Find the equations to the straight lines which pass through the point (-2, 3) and cut the axes at A (a, 0) and B (0, b) so that a+b=2

Find the equation of the straight line which passes through the origin and the point of intersection of the lines ax+by+c=0 and a'x+b'y+c'=0 .

A curve y=f(x) passes through (1,1) and tangent at P(x , y) cuts the x-axis and y-axis at A and B , respectively, such that B P : A P=3, then (a) equation of curve is x y^(prime)-3y=0 (b) normal at (1,1) is x+3y=4 (c) curve passes through 2, 1/8 (d) equation of curve is x y^(prime)+3y=0

Find the vector equation of line passing through A(3, 4, -7) and B(1, -1, 6) . Also, find its cartesian equations.

A tangent and a normal to a curve at any point P meet the x and y axes at A, B and C, D respectively. Find the equation of the curve passing through (1, 0) if the centre of circle through O.C, P and B lies on the line y = x (where O is the origin).

Find the equation of a line passing through the points (7, -3) and (2, -2) . If this line meets x-axis at point P and y-axis at point Q, find the co-ordinates of points P and Q.

Write down the equation of the line whose gradient is 3/2 and which passes through P, where P divides the line segment joining A(-2, 6) and B(3,-4) in the ratio 2 : 3.

Obtain the equation of the circle, centre (1, 0), which passes through the point P(3, 1 (1)/(2) ). Find also the equation of the equal circle which touches the given circle externally at P.