Parabolas \[y^2=4a(x-c)\] and \[x^2=4a(y-c')\] where c and c' are variables and touch each other. Locus of their point of contact is :- \[a)xy=a^2\] \[b)xy=2a^2\] \[c)xy=4a^2\] d) None of these

Please post the solution in DETAIL...

Parabolas \[y^2=4a(x-c)\] and \[x^2=4a(y-c')\] where c and c' are variables and touch each other. Locus of their point of contact is :- \[a)xy=a^2\] \[b)xy=2a^2\] \[c)xy=4a^2\] d) None of these

Please post the solution in DETAIL...

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestSlope of tangent at point of contact should be same for both the curves.Hence for both the curves take derivative of y with respect to x, substitute the point of contact in the expression obtained by the differentiation and equate.You will then get the required locus as xy=4* (square of a) – Indraneel Mukhopadhyaya · 1 year, 1 month ago

Log in to reply

You can find y in terms of x, a, andc' from eqn.2 . Now substitute it in the first eqn to get the soln... – Vishal Ramesh · 1 year, 12 months ago

Log in to reply

can you clarify something please:

if \(c\) and \(c'\) are variables, wouldn't the locus correspond to a 3 variable equation?

otherwise, considering them as constants, i get \(c\) as answer – Aritra Jana · 1 year, 12 months ago

Log in to reply