" 21.Show that the equation of a parabola in the standard form is "y^(2)=4ax

Derive the equation of a parabola in the standard form y^(2)=4ax with diagram.

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

Show that the equation of tangent to the parabola y^(2) = 4ax " at " (x_(1), y_(1)) " is " y y_(1)= 2a(x + x_(1))

Show that the equation of the tangent to the parabola y^(2) = 4 ax at (x_(1), y_(1)) is y y_(1) = 2a(x + x_(1)) .

(a)Define a parabola and derive its equation in the standard form y^2=4ax

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

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

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 its (y-y_1)(y-y_2)=y^2-4ax.

Show that the locus of the mid-points of all chords passing through the vertices of the parabola y^(2) =4ax is the parabola y^(2)=2ax .

Show that the locus of the mid-points of all chords passing through the vertices of the parabola y^(2) =4ax is the parabola y^(2)=2ax .