Question

The circle $${x^2} + {y^2} + 2\lambda x = 0,\,\lambda \, \in \,R,$$      touches the parabola $${y^2} = 4x$$  externally. Then :

A. $$\lambda > 0$$  
B. $$\lambda < 0$$
C. $$\lambda > 1$$
D. none of these
Answer :   $$\lambda > 0$$
Solution :
Parabola mcq solution image
The graph shows $$\lambda > 0.$$

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

Practice More Releted MCQ Question on
Parabola

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GeometryStraight LinesCircleParabolaEllipseHyperbolaLocus3D Geometry and VectorsThree Dimensional Geometry
TrigonometryTrigonometric Ratio and IdentitiesTrignometric EquationsProperties and Solutons of TriangleInverse Trigonometry Function