a double ordinate of the parabola y pow 2 8px is of length

A double ordinate of the parabola $${y^2} = 8px$$ is of length $$16p.$$ The angle subtended by it at the vertex of the parabola is :

A. $$\frac{\pi }{4}$$

B. $$\frac{\pi }{2}$$

C. $$\frac{\pi }{3}$$

D. none of these

Answer : $$\frac{\pi }{2}$$

Solution :
Parabola mcq solution image

$$\eqalign{ & {\text{Clearly,}}\,\,A = \left( {8p,\,8p} \right){\text{ and }}B = \left( {8p,\, - 8p} \right) \cr & {\text{Also, }}V = \left( {0,\,0} \right) \cr & 'm'{\text{ of }}AV = 1;\,\,\,\,'m'{\text{ of }}BV = - 1 \cr & {\text{Therefore, }}AV \bot BV \cr} $$

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

A double ordinate of the parabola $${y^2} = 8px$$ is of length $$16p.$$ The angle subtended by it at the vertex of the parabola 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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Parabola

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A double ordinate of the parabola $${y^2} = 8px$$ is of length $$16p.$$ The angle subtended by it at the vertex of the parabola 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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Geometry >> Parabola

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