JEE Main & Advanced
Sample Paper
JEE Main Sample Paper-14
question_answer
The minimum and maximum distance of a point (1, 2) from the ellipse \[4{{x}^{2}}+9{{y}^{2}}+8x-36y+4=0\] are k and K, then \[(K-k)\] is equal to
A) 4 units
B) 5 units
C) 6 units
D) 7 units
Correct Answer:
A
Solution :
Given equation can be rewritten as \[\frac{{{(x+1)}^{2}}}{9}+\frac{{{(y-2)}^{2}}}{4}=1\] Can be rewritten as Whose centre is (-1, 2) and the axis is parallel to x-axis. Vertices are (2, 2) and (-4, 2) and the point (1, 2) lies inside the ellipse. Minimum distance \[=-1=1=PA=k\] Maximum distance \[=PA'=K=5\] \[\therefore \] \[K-k=5-1=4\] units