If The Line ax + by + c = 0 Is A Normal To The Curve xy = 1 Then

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

SPEAK TO COUNSELLOR ? CLICK HERE

Question

If the line ax + by + c = 0 is a normal to the curve xy = 1 then

Solution

Correct option is

a > 0, b < 0 & a < 0, > 0

ax + by + c = 0

Normal to xy = 1   

            

   

            

  

  

So sign of a and sign of b are opposite.

  

You could have also argued that us 

          

⇒ Decreasing function  

  Slope < 0 always ⇒ Slope of Normal > 0 always  

⇒ Sign of a and b must be opposite. 

SIMILAR QUESTIONS

Q1

f : R âŸ¶ R be a differentiable function  x Ïµ R. If tangent drawn to the curve at any point x Ïµ (ab) always lie below the curve then

Q2

A lamp of negliligible height is placed on the ground ‘l1’ m away from a wall. A man ‘l2’ m tall is walking at a speed of  m/sec from the lamp to the nearest point on the well. When he is midway between the lamp and the wall, the rate of change in the length of his shadow on the wall is

 

Q3

Consider the parabola y2 = 4xA = (4, –4) and B = (9, 6) be two fixed points on the parabola. Let ‘C’ be moving point on the parabola between A and B such that the area of triangle ABC is maximum, then coordinate of ‘C’ is

Q4

If the rate of change of volume of a sphere is the same as rate of change of its radius, then radius, is equal to

Q5

A spherical balloon is pumped at the constant rate of 3 m3/min. The rate of increase of its surface area as certain instant is found to be 5 m2/min. At this instant it’s radius is equal to

Q6

The third derivative of a function f’’(x) vanishes for all x. If f (0) = 1, f’ (1) = 2 and f’’ = –1, then f (x) is equal to 

Q7

The chord joining the points where x = p and x = q on the curve ax2 + bx + c is parallel to the tangent at the point on the curve whose abscissa is 

Q8

If the tangent at (1, 1) on y2 = x (2 – x)2 meets the curve again at P, then is

Q9

The distance between the origin and the normal to the curve

y = e2x + x2 at x = 0 is

Q10

The point of intersection of the tangents drawn to the curve x2y = 1 – y at the points where it is meet by the curve xy = 1 – y is given by