A line `A B` makes intercepts of lengths `aa n db` on the coordinate axes. Find the equation of the parabola passing through `A ,B ,` and the origin, if `A B` is the shortest focal chord of the parabola.

Length of the shortest normal chord of the parabola y^2=4ax is

Find the equation of the line passing through (4,5) and making equal intercept in the axes.

Find equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes.

Find the equations of the circles which pass through the origin and cut off chords of length a from each of the lines y=xa n dy=-x

Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

Find the equation of a straight line Passing through (-8, 4) and making equal intercepts on the coordinate axes.

Consider the points A(2,3) and B (4,5) i. Find the slope of the line passing through the points A and B. ii. Find the equation of the line passing through A and B. iii. Find the x-intercept of the above line.

Find the equation of the parabola with vertex at the origin , passing through (2,-3) and symmetric about x-axis.

Find the equation of the circle passing through the origin and cutting intercepts of lengths 3 units and 4 unitss from the positive exes.