The parabola `y^(2) = 2ax ` gose through the point of intersection of `(x)/(3)+(y)/(2)=1` and `(x)/(2) +(y)/(3)=1` . Find its focus .

If a + bne 0 , find the coordinates of focus and the length of latus rectum of the parabola y^(2) = 2 mx which passes through the point of intersection of the straight lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 .

If the parabola y^2 = ax passes through (3,2) then the focus is

A variable straight line through the point of intersection of the two lines (x)/(3)+(y)/(2)=1and(x)/(2)+(y)/(3)=1 meets the coordinate axes at A and B . Find the locus of the middle point of AB.

If the parabola y^(2) = 4 ax passes through the point of intersection of the straight lines 3x + y + 5 = 0 and x + 3y - 1 = 0 , find the coordinates of its focus and the length of its latus rectum .

If the parabola y^(2)=4ax passes through the point of intersection of the straight lines 3x+y+5=0 and x+3y-1=0, find the co-ordinates of its focus and the length of its latus rectum.

Find the equation of the line passing through the intersection of (x-1)/(2)=(y-2)/(-3)=(z-3)/(4) and (x-4)/(5)=(y-1)/(2)=z and also through the point (2,1,-2)

If y_(1) and y_(2) are the ordinates of two points P and Q on the parabola y^(2)=4 a x and y_(3) is the ordinate of the point of intersection of the tangents at P and Q then, y_(1), y_(3) and y_(2) are in

Consider the parabolas y^2=4x , x^2=4y Find the point of intersection of the two parabolas.

Show that the equation of the chord of the parabola y^(2) = 4ax through the points (x_(1),y_(1)) and (x_(2),y_(2)) on it is (y-y_(1))(y-y_(2)) = y^(2) - 4ax

If a circle passes through the points of intersection of the axes with the lines ax-y+1=0 and x-2y+3=0 then a=