Question
Question: The point of the curve 3x<sup>2</sup> –4y<sup>2</sup> = 72 which is nearest to the line 3x + 2y – 1 ...
The point of the curve 3x2 –4y2 = 72 which is nearest to the line 3x + 2y – 1 = 0 is:
A
(+6, 3)
B
(6, –3)
C
(6, 6)
D
(6, 5)
Answer
(6, –3)
Explanation
Solution
For the nearest point on the curve, tangent drawn to curve at that point should be parallel to the given line
\ 6x1 – 8y1 (dxdy)(x1,y1)= 0
Ž (dxdy)= +43. y1x1= –23
Ž x1 = –2y1
which satisfy 3x2 –4y2 = 72
Ž 12y12 –4y12 = 72
Ž y12 = 9
Ž y1 = ± 3
Ž x1 = ± 6
Hence required points are (–6, 3) and (6, –3).