the vertex of the parabola y pow 2 8x is at the centre of a

The vertex of the parabola $${y^2} = 8x$$ is at the centre of a circle and the parabola cuts the circle at the ends of its latus rectum. Then the equation of the circle is :

A. $${x^2} + {y^2} = 4$$

B. $${x^2} + {y^2} = 20$$

C. $${x^2} + {y^2} = 80$$

D. none of these

Answer : $${x^2} + {y^2} = 20$$

Solution :
Vertex $$ = \left( {0,\,0} \right)$$ The ends of latus rectum are $$\left( {2,\,4} \right)\left( {2,\, - 4} \right)$$
$$\therefore $$ centre $$ = \left( {0,\,0} \right)$$ radius $$ = \sqrt {{2^2} + {4^2}} = \sqrt {20} $$

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 vertex of the parabola $${y^2} = 8x$$ is at the centre of a circle and the parabola cuts the circle at the ends of its latus rectum. Then the equation of the circle 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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The vertex of the parabola $${y^2} = 8x$$ is at the centre of a circle and the parabola cuts the circle at the ends of its latus rectum. Then the equation of the circle 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-

Practice More Releted MCQ Question on Parabola

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Geometry >> Parabola

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Parabola