if x yk is normal to y 2 12x then k is 926003601

If $$x+y=k$$ is normal to $${y^2} = 12x,$$ then $$k$$ is-

A. $$3$$

B. $$9$$

C. $$ - 9$$

D. $$ - 3$$

Answer : $$9$$

Solution :
$$y=mx+c$$ is normal to the parabola
$${y^2} = 4ax$$ if $$c = - 2am - a{m^3}$$
Here $$m=-1, \,c=k$$ and $$a=3$$
$$\therefore c = k = - 2\left( 3 \right)\left( { - 1} \right) - 3{\left( { - 1} \right)^3} = 9$$

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