Tip:A–D to answerE for explanationV for videoS to reveal answer
The number of points on the curve y=54x5−135x4−70x3+180x2+210x at which the normal lines are parallel to x+90y+2=0 is :
- A.
4
- B.
2
(Correct Answer) - C.
0
- D.
3
Explanation
Solving:
Slope of line: −901. Normal slope mn=−901⟹ Tangent slope dxdy=90.
dxdy=270x4−540x3−210x2+360x+210=90
9x4−18x3−7x2+12x+4=0
(x−2)2(3x+1)2=0⟹x=2,x=−1/3.
Number of points =2.
Correct Option: (2)
Explanation
Solving:
Slope of line: −901. Normal slope mn=−901⟹ Tangent slope dxdy=90.
dxdy=270x4−540x3−210x2+360x+210=90
9x4−18x3−7x2+12x+4=0
(x−2)2(3x+1)2=0⟹x=2,x=−1/3.
Number of points =2.
Correct Option: (2)
