Find the equation to the axial line of the parabola represented by $x^{2} - 2 x + 4 y - 3 = 0$

Open in App

Solution

The given equation of the parabola $x^{2} - 2 x + 4 y - 3 = 0$ can be written as $x^{2} - 2 x + 1 + 4 y - 4 = 0 \Rightarrow (x - 1)^{2} = - 4 (y - 1)$ .......(1).
Equation (1) represents the equation of a parabola whose centere is at $(1, 1)$ and axis parallel to $y$ axis and which passes through the centre of the parabola.
So the equation of axial line to the parabola (1) is $y = 1$ .

Suggest Corrections

Similar questions

Q. Find

k

, if the line

x + 2 = 0

is one of the lines represented by the equation

x^{2} + 2 x y + 4 y + k = 0

If the line $m (x - 1) - m^{2} (y - 1) + 1 = 0$ is a tangent to a parabola for any real value of m, then the equation of the parabola is

Q. The equation

x^{2} + y^{2} - 2 x + 4 y + 5 = 0

represents

Find the equation of circle which touches $2 x - y + 3 = 0$ and pass through the points of intersection of the line $x + 2 y - 1 = 0$ and the circle $x^{2} + y^{2} - 2 x + 1 = 0$

Q. Find the equation of the tangents to the circle

x^{2} + y^{2} - 2 x - 4 y - 4 = 0

which are (i) parallel,
(ii) perpendicular to the line

3 x - 4 y - 1 = 0

Join BYJU'S Learning Program

Find the equation to the axial line of the parabola represented by x2−2x+4y−3=0

Find the equation to the axial line of the parabola represented by $x^{2} - 2 x + 4 y - 3 = 0$