CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Director Circle and directrix are same for a parabola



A

True

loader
B

False

loader

Solution

The correct option is B

True


The locus of point of intersection of perpendicular tangents to a parabola is the director circle.

We know that pair of tangents from (h,k) to the parabola y2 = 4ax will be T2 = SS

T = yk  2a (x + h)

S = y2  4ax

S = k2  4ah

(yk  2a (x + h))2 = (y2  4ax) (k2  4ah)

In this equation of pair of straight lines to be perpendicular sum of coefficients should be 0.

Therefore, 4ah + 4a2 = 0

 h = a

Therefore the locus of intersection of pair of tangents that are perpendicular to each other

is x = a.

In case of parabola this is nothing but the directrix which can be viewed as a circle with infinite radius. For the parabola y2 = 4ax this is x + a = 0.


Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image