a ray of light moving parallel to the x axis gets reflected

A ray of light moving parallel to the $$x$$-axis gets reflected from a parabolic mirror whose equation is $${\left( {y - 2} \right)^2} = 4\left( {x + 1} \right).$$ After reflection, the ray must pass through the point :

A. $$\left( {0,\,2} \right)$$

B. $$\left( {2,\,0} \right)$$

C. $$\left( {0,\, - 2} \right)$$

D. $$\left( {-1,\,2} \right)$$

Answer : $$\left( {0,\,2} \right)$$

Solution :
The equation of the axis of the parabola is $$y - 2 = 0,$$ which is parallel to the $$x$$-axis. So, a ray parallel to the $$x$$-axis is parallel to the axis of the parabola. We know that any ray parallel to the axis of a parabola passes through the focus after reflection. Here $$\left( {0,\,2} \right)$$ is the focus.

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

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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

A ray of light moving parallel to the $$x$$-axis gets reflected from a parabolic mirror whose equation is $${\left( {y - 2} \right)^2} = 4\left( {x + 1} \right).$$ After reflection, the ray must pass through the point :

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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Parabola

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A ray of light moving parallel to the $$x$$-axis gets reflected from a parabolic mirror whose equation is $${\left( {y - 2} \right)^2} = 4\left( {x + 1} \right).$$ After reflection, the ray must pass through the point :

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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Releted MCQ Question on
Geometry >> Parabola

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Parabola