Question

Two variable curves C1 : y2 = 4a (x – b1) and C2 : x2 = 4a (y – b2) where ‘a’ is a given positive real no. and b1 and b2 are variable such that C1 and C2 are tangents to each other at point of contact then locus of point of contact is:

Solution

Correct option is

xy = 4a2

             

  

b1, b2 are variables, such that C1 and C2 are tan

find locus of point of contact 

         

At the point of contact, since the curves are tangent to each other

       

SIMILAR QUESTIONS

Q1

Let f (x) = ax5 + bx4 + cx3 + dx2 + ex, where abcde Ïµ R and f (x) = 0 has a positive root α, then 

Q2

Between any two real roots of the equation ex sin x – 1 = 0, the equation excos x + 1 = 0 has

Q3

f (x) is a polynomial of degree 4 with real coefficients such that f (x) = 0 is satisfied by x = 1, 2, 3 only, then f’(1). f’(2). f’(3) is equal to:

Q4

If f (x) is a polynomial of degree 5 with real coefficients such that  has 8 real roots then f (x) = 0 has:

Q5

If the function f (x) = | x2 + a | x | +b| has exactly three points of non-differentiability, then which of the following can be true?

Q6

If f (x) = loge x and g(x) = x2 and c Ïµ (4, 5), then  is equal to:

Q7

If the equation  has four solution then be lies in:

Q8

If the function f (x) = x3 – 9x2 + 24x + c has three real and distinct roots αβ and γ then the value of [α] + [β] + [γ] is,:

Q9

If at each point of the curve y = x3 – ax2 + x + 1 the tangents is inclined at an acute angle with the positive direction of the x-axis, a lies in the interval.

Q10

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