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