the tangents from the origin to the parabola y pow 2 4 4x

The tangents from the origin to the parabola $${y^2} + 4 = 4x$$ are inclined at :

A. $$\frac{\pi }{6}$$

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

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

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

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

Solution :
$${y^2} + 4 = 4x{\text{ or }}{y^2} = 4\left( {x - 1} \right)$$
Any tangent to it is $$y = m\left( {x - 1} \right) + \frac{1}{m}.$$ It is through the origin if $$0 = - m + \frac{1}{m}\,\,\,\, \Rightarrow m = 1,\, - 1$$
So, the two tangents are inclined at $$\frac{\pi }{2}.$$

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 tangents from the origin to the parabola $${y^2} + 4 = 4x$$ are inclined at :

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 tangents from the origin to the parabola $${y^2} + 4 = 4x$$ are inclined at :

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