the equation of the directrix of the parabola y 2 4y 4x 2 0

The equation of the directrix of the parabola $${y^2} + 4y + 4x + 2 = 0$$ is-

A. $$x = - 1$$

B. $$x = 1$$

C. $$x = - \frac{3}{2}$$

D. $$x = \frac{3}{2}$$

Answer : $$x = \frac{3}{2}$$

Solution :
$$\eqalign{ & {y^2} + 4y + 4x + 2 = 0 \cr & {y^2} + 4y + 4 = - 4x + 2 \cr & {\left( {y + 2} \right)^2} = - 4\left( {x - \frac{1}{2}} \right) \cr} $$
It is of the form $${Y^2} = - 4AX$$
whose directrix is given by $$X=A$$
$$\therefore $$ Required equation is $$x - \frac{1}{2} = 1\,\,\, \Rightarrow x = \frac{3}{2}$$

Releted MCQ Question on
Geometry >> Parabola

Releted Question 1

Consider a circle with its centre lying on the focus of the parabola $${y^2} = 2px$$ such that it touches the directrix of the parabola. Then a point of intersection of the circle and parabola is-

A. $$\left( {\frac{p}{2},\,p} \right){\text{ or }}\left( {\frac{p}{2},\, - p} \right)$$

B. $$\left( {\frac{p}{2},\, - \frac{p}{2}} \right)$$

C. $$\left( { - \frac{p}{2},\,p} \right)$$

D. $$\left( { - \frac{p}{2},\, - \frac{p}{2}} \right)$$

View Answer

Releted Question 2

The curve described parametrically by $$x = {t^2} + t + 1,\,\,y = {t^2} - t + 1$$ represents-

A. a pair of straight lines

B. an ellipse

C. a parabola

D. a hyperbola

View Answer

Releted Question 3

If $$x+y=k$$ is normal to $${y^2} = 12x,$$ then $$k$$ is-

A. $$3$$

B. $$9$$

C. $$ - 9$$

D. $$ - 3$$

View Answer

Releted Question 4

If the line $$x-1=0$$ is the directrix of the parabola $${y^2} - kx + 8 = 0,$$ then one of the values of $$k$$ is-

A. $$\frac{1}{8}$$

B. $$8$$

C. $$4$$

D. $$\frac{1}{4}$$

View Answer

The equation of the directrix of the parabola $${y^2} + 4y + 4x + 2 = 0$$ is-

Releted MCQ Question on
Geometry >> Parabola

Consider a circle with its centre lying on the focus of the parabola $${y^2} = 2px$$ such that it touches the directrix of the parabola. Then a point of intersection of the circle and parabola is-

The curve described parametrically by $$x = {t^2} + t + 1,\,\,y = {t^2} - t + 1$$ represents-

If $$x+y=k$$ is normal to $${y^2} = 12x,$$ then $$k$$ is-

If the line $$x-1=0$$ is the directrix of the parabola $${y^2} - kx + 8 = 0,$$ then one of the values of $$k$$ is-

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The equation of the directrix of the parabola $${y^2} + 4y + 4x + 2 = 0$$ is-

Releted MCQ Question on Geometry >> Parabola

Consider a circle with its centre lying on the focus of the parabola $${y^2} = 2px$$ such that it touches the directrix of the parabola. Then a point of intersection of the circle and parabola is-

The curve described parametrically by $$x = {t^2} + t + 1,\,\,y = {t^2} - t + 1$$ represents-

If $$x+y=k$$ is normal to $${y^2} = 12x,$$ then $$k$$ is-

If the line $$x-1=0$$ is the directrix of the parabola $${y^2} - kx + 8 = 0,$$ then one of the values of $$k$$ is-

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