Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

The set of points on the axis of the parabola \mathrm{ y^2-4 x-4 y+12=0} from which all three normals to the parabola are real is (k, m), where k and m is

Option: 1

k>4, m=2


Option: 2

k>5, m=0


Option: 3

k>4, m=1


Option: 4

None of these 


Answers (1)

best_answer

\mathrm{\begin{aligned} & y^2-4 x-4 y+12=0 \\ & y^2-4 y+4=4 x-8 \Rightarrow(y-2)^2=4(x-2) \\ & Y^2=4 X, Y=y-2, X=x-2 \end{aligned}}

All three normals to the parabola are real & meet the axis of parabola, therefore
X > 2a & Y = 0

\mathrm{\begin{aligned} & \Rightarrow X>2(1) \& y-2=0 \Rightarrow x-2>2 \& y=2 \\ & \Rightarrow x>4 \& y=2 \end{aligned}}

Point is (k, 2), k > 4

Posted by

Ritika Kankaria

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

Amrita BTech Admission 2025: JEE Main-based registration deadline extended to August 30
anam-khan

DASA, CSAB Special round 2 seat allotment result 2025 declared on csab.nic.in

Latest Question