the point a2a is an interior point of region bounded by the

The point $$\left( {a,\,2a} \right)$$ is an interior point of region bounded by the parabola $${x^2} = 16y$$ and the double ordinate through focus then :

A. $$a < 4$$

B. $$0 < a < 4$$

C. $$0 < a < 2$$

D. $$a > 4$$

Answer : $$0 < a < 2$$

Solution :
Parabola mcq solution image

Parabola $${x^2} = 16y,$$ axis is the $$y$$-axis, focus $$ = \left( {0,\,4} \right)$$
It is clear if point $$P\left( {a,\,2a} \right)$$ lies interior region then ordinate $$ \in \left( {0,\,4} \right) \Rightarrow 0 < 2a < 4 \Rightarrow 0 < a < 2$$

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 point $$\left( {a,\,2a} \right)$$ is an interior point of region bounded by the parabola $${x^2} = 16y$$ and the double ordinate through focus then :

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

Practice More MCQ Question on Maths Section

The point $$\left( {a,\,2a} \right)$$ is an interior point of region bounded by the parabola $${x^2} = 16y$$ and the double ordinate through focus then :

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

Practice More MCQ Question on Maths Section

Releted MCQ Question on
Geometry >> Parabola

Practice More Releted MCQ Question on
Parabola