If `a ne 0 ` and the line 2bx + 2cy + 4d = 0 is passing through the points of intersection of parabolas `y^(2) = 4ax ` and `x^(2) = 4ay` , then prove that `d^(2) = a^(2) (2b + 3c)^(2)` .

If a ne 0 and the line 2 bx +3 cy +4d=0 passes through the points of intersection of the parabolas y ^(2) =4ax and x^(2) =4 ay , then-

If a!=0 and the line 2b x+3c y+4d=0 passes through the points of intersection of the parabolas y^2=4a x and x^2=4a y , then (a) d^2+(2b+3c)^2=0 (b) d^2+(3b+2c)^2=0 (c) d^2+(2b-3c)^2=0 (d)none of these

Prove that, The line 5x + 4y = 0 passes through the point of intersection of straight lines x+2y-10 = 0, 2x + y =-5

The area (in square unit ) bounded by the parabolas y^(2) = 4ax and x^(2) = 4ay is -

If the straight line ax+y+6=0 passes through the point of intersection of the lines x+y+4=0 and 2x+3y+10=0 , find a.

If a straight line passing through the focus of the parabola y^(2) = 4ax intersectts the parabola at the points (x_(1), y_(1)) and (x_(2), y_(2)) , then prove that x_(1)x_(2)=a^(2) .

Find equation of the line parallel to the line 3x - 4y + 2 = 0 and passing through the point (-2, 3) .

Find the equation of the line passing through the point of intersection of the lines 4x + 7y - 3 = 0 " and " 2x - 3y + 1 = 0 that has equal intercepts on the axes.

If x = cy + bz, y = az + cx , z =bx + ay, then prove that x^2/(1-a^2)= y^2/(1-b^2)

The equation of the normal to the parabola y^(2) =4ax at the point (at^(2), 2at) is-